A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
National Research Council Canada - National Science Library
Thiago Antonini Alves; Ricardo Alan Verdú Ramos; Cassio Roberto Macedo Maia
2015-01-01
In this work was presented a hybrid analytical-numerical solution to hydrodynamic problem of fully developed Newtonian laminar flow inside biconical ducts employing the Generalized Integral Transform Technique (GITT...
A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
Directory of Open Access Journals (Sweden)
Thiago Antonini Alves
2015-10-01
Full Text Available In this work was presented a hybrid analytical-numerical solution to hydrodynamic problem of fully developed Newtonian laminar flow inside biconical ducts employing the Generalized Integral Transform Technique (GITT. In order to facilitate the analytical treatment and the application of the boundary conditions, a Conformal Transform was used to change the domain into a more suitable coordinate system. Thereafter, the GITT was applied on the momentum equation to obtain the velocity field. Numerical results were obtained for quantities of practical interest, such as maximum and minimum velocity, Fanning friction factor, Poiseuille number, Hagenbach factor and hydrodynamic entry length.
Directory of Open Access Journals (Sweden)
Farshid Mirzaee
2013-09-01
Full Text Available A numerical method based on an NM-set of general, hybrid of block-pulse function and Taylor series (HBT, is proposed to approximate the solution of nonlinear Volterra–Fredholm integral equations. The properties of HBT are first presented. Also, the operational matrix of integration together with Newton-Cotes nodes are utilized to reduce the computation of nonlinear Volterra–Fredholm integral equations into some algebraic equations. In addition, convergence analysis and numerical examples that illustrate the pertinent features of the method are presented.
Malakpoor, K.; Kaasschieter, E.F.; Huyghe, J.M.
2007-01-01
Abstract: The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, Int. J. Engng. Sci. 35 (1997) 793-802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous
Directory of Open Access Journals (Sweden)
Suheel Abdullah Malik
Full Text Available In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE through substitution is converted into a nonlinear ordinary differential equation (NODE. The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM, homotopy perturbation method (HPM, and optimal homotopy asymptotic method (OHAM, show that the suggested scheme is fairly accurate and viable for solving such problems.
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul
2015-01-01
In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.
Hybrid undulator numerical optimization
Energy Technology Data Exchange (ETDEWEB)
Hairetdinov, A.H. [Kurchatov Institute, Moscow (Russian Federation); Zukov, A.A. [Solid State Physics Institute, Chernogolovka (Russian Federation)
1995-12-31
3D properties of the hybrid undulator scheme arc studied numerically using PANDIRA code. It is shown that there exist two well defined sets of undulator parameters which provide either maximum on-axis field amplitude or minimal higher harmonics amplitude of the basic undulator field. Thus the alternative between higher field amplitude or pure sinusoidal field exists. The behavior of the undulator field amplitude and harmonics structure for a large set of (undulator gap)/(undulator wavelength) values is demonstrated.
Reinersman, Phillip N; Carder, Kendall L
2004-05-01
A hybrid method is presented by which Monte Carlo (MC) techniques are combined with an iterative relaxation algorithm to solve the radiative transfer equation in arbitrary one-, two-, or three-dimensional optical environments. The optical environments are first divided into contiguous subregions, or elements. MC techniques are employed to determine the optical response function of each type of element. The elements are combined, and relaxation techniques are used to determine simultaneously the radiance field on the boundary and throughout the interior of the modeled environment. One-dimensional results compare well with a standard radiative transfer model. The light field beneath and adjacent to a long barge is modeled in two dimensions and displayed. Ramifications for underwater video imaging are discussed. The hybrid model is currently capable of providing estimates of the underwater light field needed to expedite inspection of ship hulls and port facilities.
Numerical Solution of Parabolic Equations
DEFF Research Database (Denmark)
Østerby, Ole
These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory...... approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...
The Numerical Solution of an Abelian Ordinary Differential Equation ...
African Journals Online (AJOL)
In this paper we present a relatively new technique call theNew Hybrid of Adomian decomposition method (ADM) for solution of an Abelian Differential equation. The numerical results of the equation have been obtained in terms of convergent series with easily computable component. These methods are applied to solve ...
Numerical Solution for an Epicycloid Crack
Directory of Open Access Journals (Sweden)
Nik Mohd Asri Nik Long
2014-01-01
linear equations. Numerical solution for the shear stress intensity factors, maximum stress intensity, and strain energy release rate is obtained. Our results give an excellent agreement to the existing asymptotic solutions.
Numerical Solution of Differential Algebraic Equations
DEFF Research Database (Denmark)
Thomsen, Per Grove; Bendtsen, Claus
1999-01-01
Lecture notes for a PhD-course on the numerical solution of DAE's. The course was held at IMM in the autumn of 1998 and the early spring of 1999.......Lecture notes for a PhD-course on the numerical solution of DAE's. The course was held at IMM in the autumn of 1998 and the early spring of 1999....
NUMERICAL SOLUTIONS OF SOME PARAMETRIC EFFECTS DUE ...
African Journals Online (AJOL)
Dr A.B.Ahmed
ISSN 1597-6343. Numerical Solutions of Some Parametric Effects Due to Electromagnetic Wave. Scattering by an Infinite Circular Cylinder. NUMERICAL SOLUTIONS OF SOME PARAMETRIC EFFECTS DUE. TO ELECTROMAGNETIC WAVE SCATTERING BY AN INFINITE. CIRCULAR CYLINDER. *1 Suleiman A. B. and 1 ...
Automatic validation of numerical solutions
DEFF Research Database (Denmark)
Stauning, Ole
1997-01-01
differential equations, but in this thesis, we describe how to use the methods for enclosing iterates of discrete mappings, and then later use them for discretizing solutions of ordinary differential equations. The theory of automatic differentiation is introduced, and three methods for obtaining derivatives...... is the possiblility to combine the three methods in an extremely flexible way. We examine some applications where this flexibility is very useful. A method for Taylor expanding solutions of ordinary differential equations is presented, and a method for obtaining interval enclosures of the truncation errors incurred......, using this method has been developed. (ADIODES is an abbreviation of `` Automatic Differentiation Interval Ordinary Differential Equation Solver''). ADIODES is used to prove existence and uniqueness of periodic solutions to specific ordinary differential equations occuring in dynamical systems theory...
Numerical investigations of hybrid rocket engines
Betelin, V. B.; Kushnirenko, A. G.; Smirnov, N. N.; Nikitin, V. F.; Tyurenkova, V. V.; Stamov, L. I.
2018-03-01
Paper presents the results of numerical studies of hybrid rocket engines operating cycle including unsteady-state transition stage. A mathematical model is developed accounting for the peculiarities of diffusion combustion of fuel in the flow of oxidant, which is composed of oxygen-nitrogen mixture. Three dimensional unsteady-state simulations of chemically reacting gas mixture above thermochemically destructing surface are performed. The results show that the diffusion combustion brings to strongly non-uniform fuel mass regression rate in the flow direction. Diffusive deceleration of chemical reaction brings to the decrease of fuel regression rate in the longitudinal direction.
A numerical solution for a telegraph equation
Ashyralyev, Allaberen; Modanli, Mahmut
2014-08-01
In this study, the initial value problem for a telegraph equation in a Hilbert space is considered. The stability estimate for the solution of this problem is given. A first and a second order of approximation difference schemes approximately solving the initial value problem are presented. The stability estimates for the solution of these difference schemes are given. The theoretical statements for the solution of these difference schemes are supported by the results of numerical experiments.
Numerical and approximate solutions for plume rise
Krishnamurthy, Ramesh; Gordon Hall, J.
Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585-590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).
Python Classes for Numerical Solution of PDE's
Mushtaq, Asif; Olaussen, Kåre
2015-01-01
We announce some Python classes for numerical solution of partial differential equations, or boundary value problems of ordinary differential equations. These classes are built on routines in \\texttt{numpy} and \\texttt{scipy.sparse.linalg} (or \\texttt{scipy.linalg} for smaller problems).
Hybrid Solution for Integrated Trading
Directory of Open Access Journals (Sweden)
Vlad DIACONITA
2010-01-01
Full Text Available Integrated applications are complex solutions, whose complexity are determined by the economic processes they implement, the amount of data employed (millions of records grouped in hundreds of tables, databases, hundreds of GB and the number of users. Service oriented architecture (SOA, is now the most talked-about integration solution in mainstream journals, addressing both simple applications, for a department but also at enterprise level. SOA can refer to software architecture or to a way of standardizing the technical architecture of an enterprise and it shows its value when operating in several distinct and heterogeneous environments.
Numerical solution to nonlinear Tricomi equation using WENO schemes
Directory of Open Access Journals (Sweden)
Adrian Sescu
2010-09-01
Full Text Available Nonlinear Tricomi equation is a hybrid (hyperbolic-elliptic second order partial differential equation, modelling the sonic boom focusing. In this paper, the Tricomi equation is transformed into a hyperbolic system of first order equations, in conservation law form. On the upper boundary, a new mixed boundary condition for the acoustic pressure is used to avoid the inclusion of the Dirac function in the numerical solution. Weighted Essentially Non-Oscillatory (WENO schemes are used for the spatial discretization, and the time marching is carried out using the second order accurate Runge-Kutta total-variation diminishing (TVD scheme.
Numerical solution methods for viscoelastic orthotropic materials
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1988-01-01
Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.
Numerical and Experimental Investigation of Hybrid Rocket Motors Transient Behavior
Barato, Francesco
2013-01-01
As the space business is shifting from pure performances to affordability a renewed interest is growing about hybrid rocket propulsion. Hybrid rocket motors are attractive for their inherent advantages like simplicity, reliability, safety and reduced costs. Moreover hybrid motors are easy to throttle and thus they are ideal candidate when soft-landing or energy management capabilities are required. This thesis is mainly involved with a theoretical/numerical study of hybrid transie...
Numerical solution of the bidomain equations.
Linge, S; Sundnes, J; Hanslien, M; Lines, G T; Tveito, A
2009-05-28
Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra- and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysiology. However, complex mathematical models, steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scientific computing over the past 50 years has been to enable the solving of linear systems of algebraic equations that arise from discretizations of partial differential equations in an optimal manner, i.e. such that the central processing unit (CPU) effort increases linearly with the number of computational nodes. Over the past decade, such optimal methods have been introduced in the simulation of electrophysiology. This development, together with the development of affordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models, on geometries resembling a human heart. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for the solution of the bidomain model. This paper reviews the development of numerical methods for solving the bidomain model. However, the field is huge and we thus restrict our focus to developments that have been made since the year 2000.
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Ambipolar solution-processed hybrid perovskite phototransistors
Li, Feng
2015-09-08
Organolead halide perovskites have attracted substantial attention because of their excellent physical properties, which enable them to serve as the active material in emerging hybrid solid-state solar cells. Here we investigate the phototransistors based on hybrid perovskite films and provide direct evidence for their superior carrier transport property with ambipolar characteristics. The field-effect mobilities for triiodide perovskites at room temperature are measured as 0.18 (0.17) cm2 V−1 s−1 for holes (electrons), which increase to 1.24 (1.01) cm2 V−1 s−1 for mixed-halide perovskites. The photoresponsivity of our hybrid perovskite devices reaches 320 A W−1, which is among the largest values reported for phototransistors. Importantly, the phototransistors exhibit an ultrafast photoresponse speed of less than 10 μs. The solution-based process and excellent device performance strongly underscore hybrid perovskites as promising material candidates for photoelectronic applications.
Hybrid Experimental-Numerical Stress Analysis.
1983-04-01
A. 1. and Riley# W. F., Introduction to Pho hanics, Pren- tics -Hall, Englewood Cliffs# 1965P pp. 185-186. 8. Rao, G. V., "Experimental-numerical...Naw1 o a. CA *924 Loe Amnl*&. Ca 10024 Profesor T. V. Cosng Or. IF. Sm#Amv Or. M. P. gtesProfeesr Ulert pried University of Agree on"ser si pmlo
Numerical solution of ordinary differential equations
Fox, L
1987-01-01
Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numeri...
Numerical Solution of the Beltrami Equation
Porter, R. Michael
2008-01-01
An effective algorithm is presented for solving the Beltrami equation fzbar = mu fz in a planar disk. The algorithm involves no evaluation of singular integrals. The strategy, working in concentric rings, is to construct a piecewise linear mu-conformal mapping and then correct the image using a known algorithm for conformal mappings. Numerical examples are provided and the computational complexity is analyzed.
Numerical Solution of Turbulence Problems by Solving Burgers’ Equation
Directory of Open Access Journals (Sweden)
Alicia Cordero
2015-05-01
Full Text Available In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solutions as well as exact solutions for different values of viscosity are calculated, concluding that the numerical results are very close to the exact solution.
Hybrid RANS-LES using high order numerical methods
Henry de Frahan, Marc; Yellapantula, Shashank; Vijayakumar, Ganesh; Knaus, Robert; Sprague, Michael
2017-11-01
Understanding the impact of wind turbine wake dynamics on downstream turbines is particularly important for the design of efficient wind farms. Due to their tractable computational cost, hybrid RANS/LES models are an attractive framework for simulating separation flows such as the wake dynamics behind a wind turbine. High-order numerical methods can be computationally efficient and provide increased accuracy in simulating complex flows. In the context of LES, high-order numerical methods have shown some success in predictions of turbulent flows. However, the specifics of hybrid RANS-LES models, including the transition region between both modeling frameworks, pose unique challenges for high-order numerical methods. In this work, we study the effect of increasing the order of accuracy of the numerical scheme in simulations of canonical turbulent flows using RANS, LES, and hybrid RANS-LES models. We describe the interactions between filtering, model transition, and order of accuracy and their effect on turbulence quantities such as kinetic energy spectra, boundary layer evolution, and dissipation rate. This work was funded by the U.S. Department of Energy, Exascale Computing Project, under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.
Numerical solution of the Fokker-Planck equation
Energy Technology Data Exchange (ETDEWEB)
Shoucri, M. [Institut de Recherche Hydro-Quebec (IREQ), Varennes Quebec (Canada); Peysson, Y. [Association Euratom-CEA Cadarache, CEA/DSM/DRFC, 13 - Saint-Paul-lez-Durance (France); Shkarofsky, I. [MPB Technologies Inc., Quebec (Canada)
2006-06-15
A code to solve the Fokker-Planck kinetic equation for electrons and ions is presented. The electrons are treated with a relativistic collision operator. The importance of the numerical approach associated with an exact relativistic treatment for the solution of the electrons dynamic is emphasized in order to study accurately all the physics associated with the electron distribution function, as for instance the physics associated with the hot tail, the fast electron transport and the shape of the distribution function. Accurate relativistic treatment of the hot tail helps make the study of these problems less phenomenological and more physical. The pertinent equations for two different ions species, a majority ion and a minority ion population, are included in the code. The ions are treated with non-relativistic equations. The code also includes the appropriate quasi-linear operator for lower hybrid current drive, electron cyclotron heating and current drive, ion cyclotron heating for each of the ion species. This allows accurate study of synergy effects between the different sources for plasma heating and current drive. The exchange terms between the different species are included. The code includes also the option of a variable grid size for electrons and ions. (authors)
Dynamics of the east India coastal current. 2. Numerical solutions
Digital Repository Service at National Institute of Oceanography (India)
McCreary, J.P.; Han, W.; Shankar, D.; Shetye, S.R.
A linear, continuously stratified model is used to investigate the dynamics of the East India Coastal Current (EICC). Solutions are found numerically in a basin that resembles the Indian Ocean basin north of 29 degrees S, and they are forced...
Numerical solution of the one-dimensional Burgers' equation ...
Indian Academy of Sciences (India)
travelling in a viscous fluid [1]. In literature, many numerical methods have been proposed and implemented for approximating solution of the Burgers' equation. Many authors have used numerical techniques based on finite difference [1–8], finite element [9–13] and boundary element. [14] methods in attempting to solve the ...
Numerical solution of the one-dimensional Burgers' equation ...
Indian Academy of Sciences (India)
Numerical solution of the one-dimensional Burgers' equation: Implicit and fully implicit exponential finite difference methods ... Research Articles Volume 81 Issue 4 October 2013 pp 547-556 ... This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation.
Hybrid and Cooperative Positioning Solutions for Wireless Networks
Xiong, Zhoubing
2014-01-01
In this thesis, some hybrid and cooperative solutions are proposed and analyzed to locate the user in challenged scenarios, with the aim to overcome the limits of positioning systems based on single technology. The proposed approaches add hybrid and cooperative features to some conventional position estimation techniques like Kalman filter and particle filter, and fuse information from different radio frequency technologies. The concept of cooperative positioning is enhanced with hybrid techn...
Thermal equilibrium solution to new model of bipolar hybrid quantum hydrodynamics
Di Michele, Federica; Mei, Ming; Rubino, Bruno; Sampalmieri, Rosella
2017-08-01
In this paper we study the hybrid quantum hydrodynamic model for nano-sized bipolar semiconductor devices in thermal equilibrium. By introducing a hybrid version of the Bhom potential, we derive a bipolar hybrid quantum hydrodynamic model, which is able to account for quantum effects in a localized region of the device for both electrons and holes. Coupled with Poisson equation for the electric potential, the steady-state system is regionally degenerate in its ellipticity, due to the quantum effect only in part of the device. This regional degeneracy of ellipticity makes the study more challenging. The main purpose of the paper is to investigate the existence and uniqueness of the weak solutions to this new type of equations. We first establish the uniform boundedness of the smooth solutions to the modified bipolar quantum hydrodynamic model by the variational method, then we use the compactness technique to prove the existence of weak solutions to the original hybrid system by taking hybrid limit. In particular, we account for two different kinds of hybrid behaviour. We perform the first hybrid limit when both electrons and holes behave quantum in a given region of the device, and the second one when only one carrier exhibits hybrid behaviour, whereas the other one is presented classically in the whole domain. The semi-classical limit results are also obtained. Finally, the theoretical results are tested numerically on a simple toy model.
A Hybrid Mutation Chemical Reaction Optimization Algorithm for Global Numerical Optimization
Directory of Open Access Journals (Sweden)
Ransikarn Ngambusabongsopa
2015-01-01
Full Text Available This paper proposes a hybrid metaheuristic approach that improves global numerical optimization by increasing optimal quality and accelerating convergence. This algorithm involves a recently developed process for chemical reaction optimization and two adjustment operators (turning and mutation operators. Three types of mutation operators (uniform, nonuniform, and polynomial were combined with chemical reaction optimization and turning operator to find the most appropriate framework. The best solution among these three options was selected to be a hybrid mutation chemical reaction optimization algorithm for global numerical optimization. The optimal quality, convergence speed, and statistical hypothesis testing of our algorithm are superior to those previous high performance algorithms such as RCCRO, HP-CRO2, and OCRO.
Numerical approximation of random periodic solutions of stochastic differential equations
Feng, Chunrong; Liu, Yu; Zhao, Huaizhong
2017-10-01
In this paper, we discuss the numerical approximation of random periodic solutions of stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of the random periodic solution as the limit of the pull-back flow when the starting time tends to -∞ along the multiple integrals of the period. As the random periodic solution is not explicitly constructible, it is useful to study the numerical approximation. We discretise the SDE using the Euler-Maruyama scheme and modified Milstein scheme. Subsequently, we obtain the existence of the random periodic solution as the limit of the pull-back of the discretised SDE. We prove that the latter is an approximated random periodic solution with an error to the exact one at the rate of √{Δ t} in the mean square sense in Euler-Maruyama method and Δ t in the Milstein method. We also obtain the weak convergence result for the approximation of the periodic measure.
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Numerical solutions of telegraph equations with the Dirichlet boundary condition
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
Full Gradient Solution to Adaptive Hybrid Control
Bean, Jacob; Schiller, Noah H.; Fuller, Chris
2017-01-01
This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.
Introduction to the numerical solutions of Markov chains
Stewart, Williams J
1994-01-01
A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse - and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here, Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing metho...
Numerical methods for solution of singular integral equations
Boykov, I. V.
2016-01-01
This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors investigated onsidered iterative - projective methods and parallel methods for solution of singular integral equations, polysingular integral equations and multi-dimensional singular integral equations. The paper is the second part of overview of the authors works de...
Numerical Solution of Differential Algebraic Equations and Applications
DEFF Research Database (Denmark)
Thomsen, Per Grove
2005-01-01
These lecture notes have been written as part of a special course on the numerical solution of Differential Algebraic Equations and applications . The course was held at IMM in the spring of 2005. The authors of the different chapters have all taken part in the course and the chapters are written...
numerical solutions of fifth order boundary value problems using ...
African Journals Online (AJOL)
Dr A.B.Ahmed
solving these problems by employing polynomials as trial functions in the ... numerical solution of Volterra integral equations by Galerkin method. Caglar et .... and continuous on [0,1], i α ,. 2,1,0. = i and i β ,. ,1,0. = i are finite real constants. Transforming (10) – (11) to systems of ordinary differential equations, we have. 1 yy. =.
Numerical solutions of fifth order boundary value problems using ...
African Journals Online (AJOL)
Mamadu-Njoseh polynomials are polynomials constructed in the interval [-1,1] with respect to the weight function () = 2 + 1. This paper aims at applying these polynomials, as trial functions satisfying the boundary conditions, in a numerical approach for the solution of fifth order boundary value problems. For this, these ...
Moving Mesh for the Numerical Solution of Partial Differential Equations
Directory of Open Access Journals (Sweden)
OLIVEIRA, F. S.
2013-06-01
Full Text Available In this paper we present moving meshes for the numeric resolution of partial differential equations. We describe some important concepts on this topic and point to existing body of work for the solution of partial differential equations using the methods of finite volumes and finite elements, both with moving meshes.
Numerical Solution of Stochastic Nonlinear Fractional Differential Equations
El-Beltagy, Mohamed A.
2015-01-07
Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.
A Hybrid Numerical Analysis Method for Structural Health Monitoring
Forth, Scott C.; Staroselsky, Alexander
2001-01-01
A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.
Zhang, Zhizeng; Zhao, Zhao; Li, Yongtao
2016-06-01
This paper attempts to verify the correctness of the analytical displacement solution in transversely isotropic rock mass, and to determine the scope of its application. The analytical displacement solution of a circular tunnel in transversely isotropic rock mass was derived firstly. The analytical solution was compared with the numerical solution, which was carried out by FLAC3D software. The results show that the expression of the analytical displacement solution is correct, and the allowable engineering range is that the dip angle is less than 15 degrees.
Hybrid Biogeography Based Optimization for Constrained Numerical and Engineering Optimization
Directory of Open Access Journals (Sweden)
Zengqiang Mi
2015-01-01
Full Text Available Biogeography based optimization (BBO is a new competitive population-based algorithm inspired by biogeography. It simulates the migration of species in nature to share information. A new hybrid BBO (HBBO is presented in the paper for constrained optimization. By combining differential evolution (DE mutation operator with simulated binary crosser (SBX of genetic algorithms (GAs reasonably, a new mutation operator is proposed to generate promising solution instead of the random mutation in basic BBO. In addition, DE mutation is still integrated to update one half of population to further lead the evolution towards the global optimum and the chaotic search is introduced to improve the diversity of population. HBBO is tested on twelve benchmark functions and four engineering optimization problems. Experimental results demonstrate that HBBO is effective and efficient for constrained optimization and in contrast with other state-of-the-art evolutionary algorithms (EAs, the performance of HBBO is better, or at least comparable in terms of the quality of the final solutions and computational cost. Furthermore, the influence of the maximum mutation rate is also investigated.
Numerical solution of open string field theory in Schnabl gauge
Arroyo, E. Aldo; Fernandes-Silva, A.; Szitas, R.
2018-01-01
Using traditional Virasoro L 0 level-truncation computations, we evaluate the open bosonic string field theory action up to level (10 , 30). Extremizing this level-truncated potential, we construct a numerical solution for tachyon condensation in Schnabl gauge. We find that the energy associated to the numerical solution overshoots the expected value -1 at level L = 6. Extrapolating the level-truncation data for L ≤ 10 to estimate the vacuum energies for L > 10, we predict that the energy reaches a minimum value at L ˜ 12, and then turns back to approach -1 asymptotically as L → ∞. Furthermore, we analyze the tachyon vacuum expectation value (vev), for which by extrapolating its corresponding level-truncation data, we predict that the tachyon vev reaches a minimum value at L ˜ 26, and then turns back to approach the expected analytical result as L → ∞.
Cosmological solutions in generalized hybrid metric-Palatini gravity
Rosa, João Luís; Carloni, Sante; Lemos, José P. S.; Lobo, Francisco S. N.
2017-06-01
We construct exact solutions representing a Friedmann-Lemaître-Robsertson-Walker (FLRW) universe in a generalized hybrid metric-Palatini theory. By writing the gravitational action in a scalar-tensor representation, the new solutions are obtained by either making an ansatz on the scale factor or on the effective potential. Among other relevant results, we show that it is possible to obtain exponentially expanding solutions for flat universes even when the cosmology is not purely vacuum. We then derive the classes of actions for the original theory which generate these solutions.
Numerical solution of the space fractional Fokker-Planck equation
Liu, F.; Anh, V.; Turner, I.
2004-04-01
The traditional second-order Fokker-Planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of Brownian motion. Densities of α-stable type have been used to describe the probability distribution of these motions. The resulting governing equation of these motions is similar to the traditional Fokker-Planck equation except that the order α of the highest derivative is fractional. In this paper, a space fractional Fokker-Planck equation (SFFPE) with instantaneous source is considered. A numerical scheme for solving SFFPE is presented. Using the Riemann-Liouville and Grunwald-Letnikov definitions of fractional derivatives, the SFFPE is transformed into a system of ordinary differential equations (ODE). Then the ODE system is solved by a method of lines. Numerical results for SFFPE with a constant diffusion coefficient are evaluated for comparison with the known analytical solution. The numerical approximation of SFFPE with a time-dependent diffusion coefficient is also used to simulate Levy motion with α-stable densities. We will show that the numerical method of SFFPE is able to more accurately model these heavy-tailed motions.
Numerical Solution of a Model Equation of Price Formation
Chernogorova, T.; Vulkov, L.
2009-10-01
The paper [2] is devoted to the effect of reconciling the classical Black-Sholes theory of option pricing and hedging with various phenomena observed in the markets such as the influence of trading and hedging on the dynamics of an asset. Here we will discuss the numerical solution of initial boundary-value problems to a model equation of the theory. The lack of regularity in the solution as a result from Dirac delta coefficient reduces the accuracy in the numerical computations. First, we apply the finite volume method to discretize the differential problem. Second, we implement a technique of local regularization introduced by A-K. Tornberg and B. Engquist [7] for handling this equation. We derived the numerical regularization process into two steps: the Dirac delta function is regularized and then the regularized differential equation is discretized by difference schemes. Using the discrete maximum principle a priori bounds are obtained for the difference equations that imply stability and convergence of difference schemes for the problem under consideration. Numerical experiments are discussed.
SOLUTION OF THE SATELLITE TRANSFER PROBLEM WITH HYBRID MEMETIC ALGORITHM
Directory of Open Access Journals (Sweden)
A. V. Panteleyev
2014-01-01
Full Text Available This paper presents a hybrid memetic algorithm (MA to solve the problem of finding the optimal program control of nonlinear continuous deterministic systems based on the concept of the meme, which is one of the promising solutions obtained in the course of implementing the procedure for searching the extremes. On the basis of the proposed algorithm the software complex is formed in C#. The solution of satellite transfer problem is presented.
Hybrid flux splitting schemes for numerical resolution of two-phase flows
Energy Technology Data Exchange (ETDEWEB)
Flaatten, Tore
2003-07-01
This thesis deals with the construction of numerical schemes for approximating. solutions to a hyperbolic two-phase flow model. Numerical schemes for hyperbolic models are commonly divided in two main classes: Flux Vector Splitting (FVS) schemes which are based on scalar computations and Flux Difference Splitting (FDS) schemes which are based on matrix computations. FVS schemes are more efficient than FDS schemes, but FDS schemes are more accurate. The canonical FDS schemes are the approximate Riemann solvers which are based on a local decomposition of the system into its full wave structure. In this thesis the mathematical structure of the model is exploited to construct a class of hybrid FVS/FDS schemes, denoted as Mixture Flux (MF) schemes. This approach is based on a splitting of the system in two components associated with the pressure and volume fraction variables respectively, and builds upon hybrid FVS/FDS schemes previously developed for one-phase flow models. Through analysis and numerical experiments it is demonstrated that the MF approach provides several desirable features, including (1) Improved efficiency compared to standard approximate Riemann solvers, (2) Robustness under stiff conditions, (3) Accuracy on linear and nonlinear phenomena. In particular it is demonstrated that the framework allows for an efficient weakly implicit implementation, focusing on an accurate resolution of slow transients relevant for the petroleum industry. (author)
Solution of the radiative enclosure with a hybrid inverse method
Energy Technology Data Exchange (ETDEWEB)
Silva, Rogerio Brittes da; Franca, Francis Henrique Ramos [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica], E-mail: frfranca@mecanica.ufrgs.br
2010-07-01
This work applies the inverse analysis to solve a three-dimensional radiative enclosure - which the surfaces are diffuse-grays - filled with transparent medium. The aim is determine the powers and locations of the heaters to attain both uniform heat flux and temperature on the design surface. A hybrid solution that couples two methods, the generalized extremal optimization (GEO) and the truncated singular value decomposition (TSVD) is proposed. The determination of the heat sources distribution is treated as an optimization problem, by GEO algorithm , whereas the solution of the system of equation, that embodies the Fredholm equation of first kind and therefore is expected to be ill conditioned, is build up through TSVD regularization method. The results show that the hybrid method can lead to a heat flux on the design surface that satisfies the imposed conditions with maximum error of less than 1,10%. The results illustrated the relevance of a hybrid method as a prediction tool. (author)
The numerical solution of compressible fluid flow problems
Emmons, Howard W
1944-01-01
Numerical methods have been developed for obtaining the steady, adiabatic flow field of a frictionless, perfect gas about arbitrary two-dimensional bodies. The solutions include the subsonic velocity regions, the supersonic velocity regions, and the transition compression shocks, if required. Furthermore, the rotational motion and entropy changes following shocks are taken into account. Extensive use is made of the relaxation method. In this report the details of the methods of solution are emphasized so as to permit others to solve similar problems. Solutions already obtained are mentioned only by way of illustrating the possibilities of the methods described. The methods can be applied directly to wind tunnel and free air tests of arbitrary airfoil shapes at subsonic, sonic, and supersonic speeds.
Asymmetric MRI Magnet Design Using a Hybrid Numerical Method
Zhao, Huawei; Crozier, Stuart; Doddrell, David M.
1999-12-01
This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries.
A Cell-Based Finite Difference Method for the Numerical Solution of PDEs
Salih, A.; Barron, R. M.; Friedl, J.
2011-11-01
The governing partial differential equations of fluid motion are usually numerically approximated using one of three methods: Finite Difference (FD), Finite Volume (FV) or Finite Element (FE). Finding practical solutions to the governing equations of fluid mechanics is one of the most challenging problems in engineering because these equations, in most cases, form a set of coupled non-linear partial differential equations. In this research, a new cell-centred Finite Difference (CCFD) formulation is developed that is applied in each individual cell of an arbitrary mesh discretizing the solution domain. This feature allows the application of the proposed FD numerical formulation on arbitrary mesh topologies, i.e., structured, unstructured or hybrid meshes. Initially, a simple test case is investigated to illustrate this method. The numerical results are compared with the analytical solution and/or a traditional FD solution. Lastly, two additional test cases are conducted to illustrate the ability of the CCFD method to handle mixed boundary types and its extendibility to other types of elliptic boundary value problems.
High mobility solution-processed hybrid light emitting transistors
Walker, Bright; Ullah, Mujeeb; Chae, Gil Jo; Burn, Paul L.; Cho, Shinuk; Kim, Jin Young; Namdas, Ebinazar B.; Seo, Jung Hwa
2014-11-01
We report the design, fabrication, and characterization of high-performance, solution-processed hybrid (inorganic-organic) light emitting transistors (HLETs). The devices employ a high-mobility, solution-processed cadmium sulfide layer as the switching and transport layer, with a conjugated polymer Super Yellow as an emissive material in non-planar source/drain transistor geometry. We demonstrate HLETs with electron mobilities of up to 19.5 cm2/V s, current on/off ratios of >107, and external quantum efficiency of 10-2% at 2100 cd/m2. These combined optical and electrical performance exceed those reported to date for HLETs. Furthermore, we provide full analysis of charge injection, charge transport, and recombination mechanism of the HLETs. The high brightness coupled with a high on/off ratio and low-cost solution processing makes this type of hybrid device attractive from a manufacturing perspective.
Random ordinary differential equations and their numerical solution
Han, Xiaoying
2017-01-01
This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor ...
Bio-based lubricants for numerical solution of elastohydrodynamic lubrication
Cupu, Dedi Rosa Putra; Sheriff, Jamaluddin Md; Osman, Kahar
2012-06-01
This paper presents a programming code to provide numerical solution of elastohydrodynamic lubrication problem in line contacts which is modeled through an infinite cylinder on a plane to represent the application of roller bearing. In this simulation, vegetable oils will be used as bio-based lubricants. Temperature is assumed to be constant at 40°C. The results show that the EHL pressure for all vegetable oils was increasing from inlet flow until the center, then decrease a bit and rise to the peak pressure. The shapes of EHL film thickness for all tested vegetable oils are almost flat at contact region.
Numerical solution of dynamic equilibrium models under Poisson uncertainty
DEFF Research Database (Denmark)
Posch, Olaf; Trimborn, Timo
2013-01-01
of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel......We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations...
A numerical solution for the diffusion equation in hydrogeologic systems
Ishii, A.L.; Healy, R.W.; Striegl, R.G.
1989-01-01
The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)
Numerical solution of High-kappa model of superconductivity
Energy Technology Data Exchange (ETDEWEB)
Karamikhova, R. [Univ. of Texas, Arlington, TX (United States)
1996-12-31
We present formulation and finite element approximations of High-kappa model of superconductivity which is valid in the high {kappa}, high magnetic field setting and accounts for applied magnetic field and current. Major part of this work deals with steady-state and dynamic computational experiments which illustrate our theoretical results numerically. In our experiments we use Galerkin discretization in space along with Backward-Euler and Crank-Nicolson schemes in time. We show that for moderate values of {kappa}, steady states of the model system, computed using the High-kappa model, are virtually identical with results computed using the full Ginzburg-Landau (G-L) equations. We illustrate numerically optimal rates of convergence in space and time for the L{sup 2} and H{sup 1} norms of the error in the High-kappa solution. Finally, our numerical approximations demonstrate some well-known experimentally observed properties of high-temperature superconductors, such as appearance of vortices, effects of increasing the applied magnetic field and the sample size, and the effect of applied constant current.
Accurate and efficient numerical solutions for elliptic obstacle problems
Directory of Open Access Journals (Sweden)
Philku Lee
2017-02-01
Full Text Available Abstract Elliptic obstacle problems are formulated to find either superharmonic solutions or minimal surfaces that lie on or over the obstacles, by incorporating inequality constraints. In order to solve such problems effectively using finite difference (FD methods, the article investigates simple iterative algorithms based on the successive over-relaxation (SOR method. It introduces subgrid FD methods to reduce the accuracy deterioration occurring near the free boundary when the mesh grid does not match with the free boundary. For nonlinear obstacle problems, a method of gradient-weighting is introduced to solve the problem more conveniently and efficiently. The iterative algorithm is analyzed for convergence for both linear and nonlinear obstacle problems. An effective strategy is also suggested to find the optimal relaxation parameter. It has been numerically verified that the resulting obstacle SOR iteration with the optimal parameter converges about one order faster than state-of-the-art methods and the subgrid FD methods reduce numerical errors by one order of magnitude, for most cases. Various numerical examples are given to verify the claim.
Accelerating numerical solution of stochastic differential equations with CUDA
Januszewski, M.; Kostur, M.
2010-01-01
hundreds of threads simultaneously makes it possible to speed up the computation by over two orders of magnitude, compared to a typical modern CPU. Solution method: The stochastic Runge-Kutta method of the second order is applied to integrate the equation of motion. Ensemble-averaged quantities of interest are obtained through averaging over multiple independent realizations of the system. Unusual features: The numerical solution of the stochastic differential equations in question is performed on a GPU using the CUDA environment. Running time: < 1 minute
Numerical Comparison of Solutions of Kinetic Model Equations
Directory of Open Access Journals (Sweden)
A. A. Frolova
2015-01-01
Full Text Available The collision integral approximation by different model equations has created a whole new trend in the theory of rarefied gas. One widely used model is the Shakhov model (S-model obtained by expansion of inverse collisions integral in a series of Hermite polynomials up to the third order. Using the same expansion with another value of free parameters leads to a linearized ellipsoidal statistical model (ESL.Both model equations (S and ESL have the same properties, as they give the correct relaxation of non-equilibrium stress tensor components and heat flux vector, the correct Prandtl number at the transition to the hydrodynamic regime and do not guarantee the positivity of the distribution function.The article presents numerical comparison of solutions of Shakhov equation, ESL- model and full Boltzmann equation in the four Riemann problems for molecules of hard spheres.We have considered the expansion of two gas flows, contact discontinuity, the problem of the gas counter-flows and the problem of the shock wave structure. For the numerical solution of the kinetic equations the method of discrete ordinates is used.The comparison shows that solution has a weak sensitivity to the form of collision operator in the problem of expansions of two gas flows and results obtained by the model and the kinetic Boltzmann equations coincide.In the problem of the contact discontinuity the solution of model equations differs from full kinetic solutions at the point of the initial discontinuity. The non-equilibrium stress tensor has the maximum errors, the error of the heat flux is much smaller, and the ESL - model gives the exact value of the extremum of heat flux.In the problems of gas counter-flows and shock wave structure the model equations give significant distortion profiles of heat flux and non-equilibrium stress tensor components in front of the shock waves. This behavior is due to fact that in the models under consideration there is no dependency of the
LED-based Photometric Stereo: Modeling, Calibration and Numerical Solutions
DEFF Research Database (Denmark)
Quéau, Yvain; Durix, Bastien; Wu, Tao
2018-01-01
We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to be directional, which is very difficult to achieve...... in practice. Rather, we use light-emitting diodes to illuminate the scene to be reconstructed. Such point light sources are very convenient to use, yet they yield a more complex photometric stereo model which is arduous to solve. We first derive in a physically sound manner this model, and show how...... approach is not established. The second one directly recovers the depth, by formulating photometric stereo as a system of nonlinear partial differential equations (PDEs), which are linearized using image ratios. Although the sequential approach is avoided, initialization matters a lot and convergence...
Numerical simulation of active track tensioning system for autonomous hybrid vehicle
Mȩżyk, Arkadiusz; Czapla, Tomasz; Klein, Wojciech; Mura, Gabriel
2017-05-01
One of the most important components of a high speed tracked vehicle is an efficient suspension system. The vehicle should be able to operate both in rough terrain for performance of engineering tasks as well as on the road with high speed. This is especially important for an autonomous platform that operates either with or without human supervision, so that the vibration level can rise compared to a manned vehicle. In this case critical electronic and electric parts must be protected to ensure the reliability of the vehicle. The paper presents a dynamic parameters determination methodology of suspension system for an autonomous high speed tracked platform with total weight of about 5 tonnes and hybrid propulsion system. Common among tracked vehicles suspension solutions and cost-efficient, the torsion-bar system was chosen. One of the most important issues was determining optimal track tensioning - in this case an active hydraulic system was applied. The selection of system parameters was performed with using numerical model based on multi-body dynamic approach. The results of numerical analysis were used to define parameters of active tensioning control system setup. LMS Virtual.Lab Motion was used for multi-body dynamics numerical calculation and Matlab/SIMULINK for control system simulation.
Stress analysis and damage evaluation of flawed composite laminates by hybrid-numerical methods
Yang, Yii-Ching
1992-01-01
Structural components in flight vehicles is often inherited flaws, such as microcracks, voids, holes, and delamination. These defects will degrade structures the same as that due to damages in service, such as impact, corrosion, and erosion. It is very important to know how a structural component can be useful and survive after these flaws and damages. To understand the behavior and limitation of these structural components researchers usually do experimental tests or theoretical analyses on structures with simulated flaws. However, neither approach has been completely successful. As Durelli states that 'Seldom does one method give a complete solution, with the most efficiency'. Examples of this principle is seen in photomechanics which additional strain-gage testing can only average stresses at locations of high concentration. On the other hand, theoretical analyses including numerical analyses are implemented with simplified assumptions which may not reflect actual boundary conditions. Hybrid-Numerical methods which combine photomechanics and numerical analysis have been used to correct this inefficiency since 1950's. But its application is limited until 1970's when modern computer codes became available. In recent years, researchers have enhanced the data obtained from photoelasticity, laser speckle, holography and moire' interferometry for input of finite element analysis on metals. Nevertheless, there is only few of literature being done on composite laminates. Therefore, this research is dedicated to this highly anisotropic material.
Numerical solution of Lord-Shulman thermopiezoelectricity dynamical problem
Stelmashchuk, Vitaliy; Shynkarenko, Heorhiy
2018-01-01
Using Lord-Shulman hypothesis we formulate the initial boundary value problem and its corresponding variational problem of a generalized linear thermopiezoelectricity in terms of the displacement, electrical potential, temperature increment and heat flux, which describes the dynamic behavior of the coupled mechanic, electric and heat waves in pyroelectric materials. We construct the corresponding energy balance equation and determine input data regularity for the variational problem, which guarantees the existence, uniqueness and stability of its solution in the problem energy norm. Based on these results, we propose a numerical scheme for solving this problem, which includes spatial finite element semi-discretization and one-step recurrent time integration procedures and generalizes the similar one for classic thermopiezoelectricity problem. We give the sufficient conditions on the values of the scheme parameters which guarantee properties of conservatism and unconditional stability of the scheme. The rest of the article is devoted to the analysis of performed numerical experiments with 1D model problem and their results are then compared with the ones obtained by the other researchers.
Cilfone, Nicholas A; Kirschner, Denise E; Linderman, Jennifer J
2015-03-01
Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level.
Multivariate Numerical Taxonomy of Mentha Species, Hybrids, Varieties and Cultivars
ŠARIĆ-KUNDALIĆ, Broza; FIALOVÁ, Silvia; Dobeš, Christoph; ÖLZANT, Silvester; TEKEĽOVÁ, Daniela; GRANČAI, Daniel; Reznicek, Gottfried; Saukel, Johannes
2009-01-01
Hercegovina and Slovakia is presented. Following a population-based approach and using hierarchical cluster analyses the following basic species and hybrids corresponding to exclusive branches, i.e. groups, in the constructed hierarchies were recognized: Mentha aquatica, M. spicata, M. arvensis, M. longifolia, M. rotundifolia, M. × piperita, M. × villosa, M. × verticillata, M. × gentillis, M. × gracilis and M. pulegium. These groups were independently found by separate analyses of the sampled...
A hybrid ICT-solution for smart meter data analytics
DEFF Research Database (Denmark)
Liu, Xiufeng; Nielsen, Per Sieverts
2016-01-01
conditions and user information, which makes the data sets very sizable and the analytics complex. Data mining and emerging cloud computing technologies make collecting, processing, and analyzing the so-called big data possible. This paper proposes an innovative ICT-solution to streamline smart meter data...... analytics. The proposed solution offers an information integration pipeline for ingesting data from smart meters, a scalable platform for processing and mining big data sets, and a web portal for visualizing analytics results. The implemented system has a hybrid architecture of using Spark or Hive for big......Smart meters are increasingly used worldwide. Smart meters are the advanced meters capable of measuring energy consumption at a fine-grained time interval, e.g., every 15 min. Smart meter data are typically bundled with social economic data in analytics, such as meter geographic locations, weather...
A hybrid ICT-solution for smart meter data analytics
DEFF Research Database (Denmark)
Liu, Xiufeng; Nielsen, Per Sieverts
2016-01-01
Smart meters are increasingly used worldwide. Smart meters are the advanced meters capable of measuring energy consumption at a fine-grained time interval, e.g., every 15 min. Smart meter data are typically bundled with social economic data in analytics, such as meter geographic locations, weather...... conditions and user information, which makes the data sets very sizable and the analytics complex. Data mining and emerging cloud computing technologies make collecting, processing, and analyzing the so-called big data possible. This paper proposes an innovative ICT-solution to streamline smart meter data...... analytics. The proposed solution offers an information integration pipeline for ingesting data from smart meters, a scalable platform for processing and mining big data sets, and a web portal for visualizing analytics results. The implemented system has a hybrid architecture of using Spark or Hive for big...
Numerical modelling of the binary alloys solidification with solutal undercooling
Directory of Open Access Journals (Sweden)
T. Skrzypczak
2008-03-01
Full Text Available In thc papcr descrip~ion of mathcmn~icaI and numerical modcl of binay alloy sot idification is prcscntcd. Mctal alloy consisting of maincomponent and solulc is introduced. Moving, sharp solidification rmnt is assumcd. Conaitulional undcrcooling phcnomcnon is tnkcn intoconsidcralion. As a solidifica~ionf ront advances, solutc is rcdistributcd at thc intcrfacc. Commonly, solutc is rejccted into Itlc liquid. whcrcit accumuIatcs into solittc boundary laycr. Depending on thc tcmpcrature gradient, such tiquid may be undcrcoolcd hclow its mclting point,cvcn though it is hot~crth an liquid at thc Front. This phcnomcnon is orten callcd constitutional or soIr~talu ndcrcool ing, to cmphasizc that itariscs from variations in solutal distribution or I iquid. An important conscqucncc of this accurnulntion of saIutc is that it can cause thc frontto brcak down into cclls or dendri~csT. his occurs bccausc thcrc is a liquid ahcad of thc front with lowcr solutc contcnt, and hcncc a highcrme1 ting tcmpcraturcs than liquid at thc front. In rhc papcr locarion and shapc of wndcrcoolcd rcgion dcpcnding on solidification pararnctcrsis discussed. Nurncrical mcthod basing on Fini tc Elelncnt Mctbod (FEM allowi~lgp rcdiction of breakdown of inoving planar front duringsolidification or binary alloy is proposed.
A Hybrid Smartphone Indoor Positioning Solution for Mobile LBS
Directory of Open Access Journals (Sweden)
Heidi Kuusniemi
2012-12-01
Full Text Available Smartphone positioning is an enabling technology used to create new business in the navigation and mobile location-based services (LBS industries. This paper presents a smartphone indoor positioning engine named HIPE that can be easily integrated with mobile LBS. HIPE is a hybrid solution that fuses measurements of smartphone sensors with wireless signals. The smartphone sensors are used to measure the user’s motion dynamics information (MDI, which represent the spatial correlation of various locations. Two algorithms based on hidden Markov model (HMM problems, the grid-based filter and the Viterbi algorithm, are used in this paper as the central processor for data fusion to resolve the position estimates, and these algorithms are applicable for different applications, e.g., real-time navigation and location tracking, respectively. HIPE is more widely applicable for various motion scenarios than solutions proposed in previous studies because it uses no deterministic motion models, which have been commonly used in previous works. The experimental results showed that HIPE can provide adequate positioning accuracy and robustness for different scenarios of MDI combinations. HIPE is a cost-efficient solution, and it can work flexibly with different smartphone platforms, which may have different types of sensors available for the measurement of MDI data. The reliability of the positioning solution was found to increase with increasing precision of the MDI data.
A hybrid smartphone indoor positioning solution for mobile LBS.
Liu, Jingbin; Chen, Ruizhi; Pei, Ling; Guinness, Robert; Kuusniemi, Heidi
2012-12-12
Smartphone positioning is an enabling technology used to create new business in the navigation and mobile location-based services (LBS) industries. This paper presents a smartphone indoor positioning engine named HIPE that can be easily integrated with mobile LBS. HIPE is a hybrid solution that fuses measurements of smartphone sensors with wireless signals. The smartphone sensors are used to measure the user's motion dynamics information (MDI), which represent the spatial correlation of various locations. Two algorithms based on hidden Markov model (HMM) problems, the grid-based filter and the Viterbi algorithm, are used in this paper as the central processor for data fusion to resolve the position estimates, and these algorithms are applicable for different applications, e.g., real-time navigation and location tracking, respectively. HIPE is more widely applicable for various motion scenarios than solutions proposed in previous studies because it uses no deterministic motion models, which have been commonly used in previous works. The experimental results showed that HIPE can provide adequate positioning accuracy and robustness for different scenarios of MDI combinations. HIPE is a cost-efficient solution, and it can work flexibly with different smartphone platforms, which may have different types of sensors available for the measurement of MDI data. The reliability of the positioning solution was found to increase with increasing precision of the MDI data.
Milne, a routine for the numerical solution of Milne's problem
Rawat, Ajay; Mohankumar, N.
2010-11-01
The routine Milne provides accurate numerical values for the classical Milne's problem of neutron transport for the planar one speed and isotropic scattering case. The solution is based on the Case eigen-function formalism. The relevant X functions are evaluated accurately by the Double Exponential quadrature. The calculated quantities are the extrapolation distance and the scalar and the angular fluxes. Also, the H function needed in astrophysical calculations is evaluated as a byproduct. Program summaryProgram title: Milne Catalogue identifier: AEGS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 701 No. of bytes in distributed program, including test data, etc.: 6845 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC under Linux or Windows Operating system: Ubuntu 8.04 (Kernel version 2.6.24-16-generic), Windows-XP Classification: 4.11, 21.1, 21.2 Nature of problem: The X functions are integral expressions. The convergence of these regular and Cauchy Principal Value integrals are impaired by the singularities of the integrand in the complex plane. The DE quadrature scheme tackles these singularities in a robust manner compared to the standard Gauss quadrature. Running time: The test included in the distribution takes a few seconds to run.
Runkel, Robert L.; Chapra, Steven C.
1993-01-01
Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.
Lindsay, A. E.; Spoonmore, R. T.; Tzou, J. C.
2016-10-01
A hybrid asymptotic-numerical method is presented for obtaining an asymptotic estimate for the full probability distribution of capture times of a random walker by multiple small traps located inside a bounded two-dimensional domain with a reflecting boundary. As motivation for this study, we calculate the variance in the capture time of a random walker by a single interior trap and determine this quantity to be comparable in magnitude to the mean. This implies that the mean is not necessarily reflective of typical capture times and that the full density must be determined. To solve the underlying diffusion equation, the method of Laplace transforms is used to obtain an elliptic problem of modified Helmholtz type. In the limit of vanishing trap sizes, each trap is represented as a Dirac point source that permits the solution of the transform equation to be represented as a superposition of Helmholtz Green's functions. Using this solution, we construct asymptotic short-time solutions of the first-passage-time density, which captures peaks associated with rapid capture by the absorbing traps. When numerical evaluation of the Helmholtz Green's function is employed followed by numerical inversion of the Laplace transform, the method reproduces the density for larger times. We demonstrate the accuracy of our solution technique with a comparison to statistics obtained from a time-dependent solution of the diffusion equation and discrete particle simulations. In particular, we demonstrate that the method is capable of capturing the multimodal behavior in the capture time density that arises when the traps are strategically arranged. The hybrid method presented can be applied to scenarios involving both arbitrary domains and trap shapes.
A Numerical Approach for Hybrid Simulation of Power System Dynamics Considering Extreme Icing Events
DEFF Research Database (Denmark)
Chen, Lizheng; Zhang, Hengxu; Wu, Qiuwei
2017-01-01
The global climate change leads to more extreme meteorological conditions such as icing weather, which have caused great losses to power systems. Comprehensive simulation tools are required to enhance the capability of power system risk assessment under extreme weather conditions. A hybrid...... numerical simulation scheme integrating icing weather events with power system dynamics is proposed to extend power system numerical simulation. A technique is developed to efficiently simulate the interaction of slow dynamics of weather events and fast dynamics of power systems. An extended package for PSS....../E enabling hybrid simulation of icing event and power system disturbance is developed, based on which a hybrid simulation platform is established. Numerical studies show that the functionality of power system simulation is greatly extended by taking into account the icing weather events....
Dynamic force profile in hydraulic hybrid vehicles: a numerical investigation
Mohaghegh-Motlagh, Amin; Elahinia, Mohammad H.
2010-04-01
A hybrid hydraulic vehicle (HHV) combines a hydraulic sub-system with the conventional drivetrain in order to improve fuel economy for heavy vehicles. The added hydraulic module manages the storage and release of fluid power necessary to assist the motion of the vehicle. The power collected by a pump/motor (P/M) from the regenerative braking phase is stored in a high-pressure accumulator and then released by the P/M to the driveshaft during the acceleration phase. This technology is effective in significantly improving fuel-economy for heavy-class vehicles with frequent stop-and-go drive schedules. Despite improved fuel economy and higher vehicle acceleration, noise and vibrations are one of the main problems of these vehicles. The dual function P/Ms are the main source of noise and vibration in a HHV. This study investigates the dynamics of a P/M and particularly the profile and frequency-dependence of the dynamic forces generated by a bent-axis P/M unit. To this end, the fluid dynamics side of the problem has been simplified for investigating the system from a dynamics perspective. A mathematical model of a bent axis P/M has been developed to investigate the cause of vibration and noise in HHVs. The forces are calculated in time and frequency domains. The results of this work can be used to study the vibration response of the chassis and to design effective vibration isolation systems for HHVs.
New Numerical Solution of von Karman Equation of Lengthwise Rolling
Rudolf Pernis; Tibor Kvackaj
2015-01-01
The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a) by polygonal curve and (b) by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rol...
Mashayekhi, S.; Razzaghi, M.; Tripak, O.
2014-01-01
A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. PMID:24523638
Numerical solution of the stochastic parabolic equation with the dependent operator coefficient
Energy Technology Data Exchange (ETDEWEB)
Ashyralyev, Allaberen [Department of Elementary Mathematics Education, Fatih University, 34500, Istanbul (Turkey); Department of Mathematics, ITTU, Ashgabat (Turkmenistan); Okur, Ulker [Institute for Stochastics and Applications, Department of Mathematics, University of Stuttgart, 70569, Stuttgart (Germany)
2015-09-18
In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.
A Numerical Approach for Hybrid Simulation of Power System Dynamics Considering Extreme Icing Events
Chen, Lizheng; Zhang, Hengxu; Wu, Qiuwei; Terzija, Vladimir
2017-01-01
The global climate change leads to more extreme meteorological conditions such as icing weather, which have caused great losses to power systems. Comprehensive simulation tools are required to enhance the capability of power system risk assessment under extreme weather conditions. A hybrid numerical simulation scheme integrating icing weather events with power system dynamics is proposed to extend power system numerical simulation. A technique is developed to efficiently simulate the interact...
A Hybrid Location Privacy Solution for Mobile LBS
Directory of Open Access Journals (Sweden)
Ruchika Gupta
2017-01-01
Full Text Available The prevalent usage of location based services, where getting any service is solely based on the user’s current location, has raised an extreme concern over location privacy of the user. Generalized approaches dealing with location privacy, referred to as cloaking and obfuscation, are mainly based on a trusted third party, in which all the data remain available at a central server and thus complete knowledge of the query exists at the central node. This is the major limitation of such approaches; on the other hand, in trusted third-party-free framework clients collaborate with each other and freely communicate with the service provider without any third-party involvement. Measuring and evaluating trust among peers is a crucial aspect in trusted third-party-free framework. This paper exploits the merits and mitigating the shortcomings of both of these approaches. We propose a hybrid solution, HYB, to achieve location privacy for the mobile users who use location services frequently. The proposed HYB scheme is based on the collaborative preprocessing of location data and utilizes the benefits of homomorphic encryption technique. Location privacy is achieved at two levels, namely, at the proximity level and at distant level. The proposed HYB solution preserves the user’s location privacy effectively under specific, pull-based, sporadic query scenario.
Enhanced FAA-hybrid III numerical dummy model in Madymo for aircraft occupant safety assessment
Boucher, H.; Waagmeester, C.D.
2003-01-01
To improve survivability and to minimize the risk of injury to occupants in helicopter crash events, a complete Cabin Safety System concept including safety features and an enhanced FAA-Hybrid III dummy were developed within the HeliSafe project. A numerical tool was also created and validated to
Directory of Open Access Journals (Sweden)
D. Vivek
2016-11-01
Full Text Available In this paper, the improved Euler method is used for solving hybrid fuzzy fractional differential equations (HFFDE of order $q \\in (0, 1 $ under Caputo-type fuzzy fractional derivatives. This method is based on the fractional Euler method and generalized Taylor's formula. The accuracy and efficiency of the proposed method is demonstrated by solving numerical examples.
A Globally Convergent Hybrid Conjugate Gradient Method and Its Numerical Behaviors
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Yuan-Yuan Huang
2013-01-01
Full Text Available We consider a hybrid Dai-Yuan conjugate gradient method. We confirm that its numerical performance can be improved provided that this method uses a practical steplength rule developed by Dong, and the associated convergence is analyzed as well.
Numerical Solution of Magnetostatic Field of Maglev System
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Jaroslav Sobotka
2008-01-01
Full Text Available The paper deals with the design of the levitation and guidance system of the levitation train Transrapid 08 by means of QuickField 5.0 – a 2D program formagnetic electromagnetic fields solutions.
Numerical investigation of magnetic sensor for DNA hybridization detection using planar transformer
Directory of Open Access Journals (Sweden)
Sayyed M. Azimi
2007-12-01
Full Text Available This paper introduces a sensor for detection of DNA hybridization and investigates its performance by means of computer simulation. A planar transformer with spiral windings is proposed for hybridization detection. In order to detect the occurrence of hybridization, single strand target DNA’s are tagged with magnetic beads. Target DNA’s are then exposed to known single strand probe DNA’s which are immobilized on the surface of a functionalized layer in the proximity of the sensor. The primary winding of the transformer is driven by an AC current source. The voltage at the secondary winding is used for detection. Once the hybridization is occurred, a layer of magnetic material is formed and the coupling between the windings is varied. These variations are reflected into the detecting output voltage. The magnitude of the output voltage is numerically calculated in terms of geometrical and physical parameters and the parameter values resulting in maximum response are derived.
Numerical solution of boundary layer MHD flow with viscous dissipation.
Mishra, S R; Jena, S
2014-01-01
The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by fourth-order Runge-Kutta method with shooting technique. Results for velocity and temperature profiles for different values of the governing parameters have been discussed in detail with graphical representation. The numerical evaluation of skin friction and Nusselt number are also given in this paper.
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Charyyar Ashyralyyev
2015-07-01
Full Text Available This article studies the numerical solution of inverse problems for the multidimensional elliptic equation with Dirichlet-Neumann boundary conditions and Neumann type overdetermination. We present first and second order accuracy difference schemes. The stability and almost coercive stability inequalities for the solution are obtained. Numerical examples with explanation on the implementation illustrate the theoretical results.
A numerical solution of the Burgers' equation using septic B-splines
Energy Technology Data Exchange (ETDEWEB)
Ramadan, Mohamed A. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt)] e-mail: mramadan@mailer.eun.eg; El-Danaf, Talaat S. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt); Abd Alaal, Faisal E.I. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt)
2005-11-01
In this paper, numerical solutions of the nonlinear Burgers' equation are obtained by a method based on collocation of septic B-splines over finite elements. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. Numerical solutions of the modified Burgers' equation are also obtained by making a simple change of the suggested numerical scheme for the Burgers' equation. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
A numerical solution of the Burgers' equation using septic B-sp lines
Energy Technology Data Exchange (ETDEWEB)
Ramadan, Mohamed A. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt)] e-mail: mramadan@mailer.eun.eg; El-Danaf, Talaat S. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt); Abd Alaal, Faisal E.I. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt)
2005-11-01
In this paper, numerical solutions of the nonlinear Burgers' equation are obtained by a method based on collocation of septic B-sp lines over finite elements. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. Numerical solutions of the modified Burgers' equation are also obtained by making a simple change of the suggested numerical scheme for the Burgers' equation. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
A time splitting algorithm for numerical solution of Richard's equation
Namin, Masoud Montazeri; Boroomand, Mohammad Reza
2012-06-01
SummaryThe Richard's equation mathematically expressing the infiltration problem is a transport type of equation describing two different phenomena namely advection and diffusion being hyperbolic and parabolic type of differential equation, respectively each having their own physical properties thus a single numerical scheme would not essentially be suitable for both. In this paper a numerical algorithm based on time splitting or fractional step method has been proposed and described. This has allowed designing and applying some different numerical schemes more compatible with the mathematical and physical properties of the corresponding phenomenon. In advection part an implicit characteristic based method has been employed to calculate the cell face fluxes and then the new unknowns have been obtained using finite volume method (FVM) explicitly. Two different speed type quantities namely wave celerity and mass velocity have been distinguished in the advection of infiltrated water to the soil, the magnitude of the first being several times larger than the other. The implicit characteristic based method has been designed specifically to cope with the mentioned high wave celerity. An implicit numerical scheme has been employed in which the space derivative term contributed in definition of cell face flux has been discretized in fourth order accurate manner. The extra cells getting involved due to the higher order discretization have been taken in account in a way not to change the tri-diagonal matrix coefficient shape preserving the efficiency of the algorithm. The performance, accuracy and efficiency of the out coming non-iterative numerical algorithm have been successfully examined by some test cases. The relative importance of the advection and diffusion terms in the concerned transport equation and the ration of their contribution in the overall infiltrated flux also have been discussed in detail.
Numerical solutions of Einstein field equations with radial dark matter
Klimenko, Stanislav; Nikitin, Igor; Nikitina, Lialia
We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant velocities of circular motion, i.e. flat rotation curves. At smaller distances, the field switches to Newtonian regime, then to Schwarzschild regime. Deviations from Schwarzschild regime start below the gravitational radius. The dark matter prevents the creation of event horizon, instead, a spherical region possessing extremely large redshift is created. The structure of space-time for the obtained solutions is investigated and the implications for the models of the galaxies are discussed.
Novel Approaches To Numerical Solutions Of Quantum Field Theories
Petrov, D
2005-01-01
Two new approaches to numerically solving Quantum Field Theories are presented. The Source Galerkin technique is a direct approach to determining the generating functional of a theory by solving the Schwinger-Dyson equations. The properties of the Source Galerkin technique are tested by using it to determine the phase structure of the Ultralocal &phis;4 theory. A framework for applying this approach to solving O( N) Nonlinear Sigma model is constructed. The Sinc Function approximation is a highly efficient method of numerically evaluating Feynman diagrams. In the present dissertation the Sinc Function approximation is applied to fermionic fields. The Sinc expanded versions of fermion and photon propagators are derived. The accuracy of this approximation is tested by a direct comparison of the Sinc expanded propagators with exact propagators and by performing several sample calculations of one loop QED diagrams. An analysis of computational properties of the Sinc Function approach is presented.
Numerical Solution of Hamilton-Jacobi Equations in High Dimension
2012-11-23
high dimension FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA-Universita di Roma P. Aldo Moro, 2 00185 ROMA AH930...solution of Hamilton-Jacobi equations in high dimension AFOSR contract n. FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA
Analysis of Linear Piecewise Constant Delay Systems Using a Hybrid Numerical Scheme
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H. R. Marzban
2016-01-01
Full Text Available An efficient computational technique for solving linear delay differential equations with a piecewise constant delay function is presented. The new approach is based on a hybrid of block-pulse functions and Legendre polynomials. A key feature of the proposed framework is the excellent representation of smooth and especially piecewise smooth functions. The operational matrices of delay, derivative, and product corresponding to the mentioned hybrid functions are implemented to transform the original problem into a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the proposed numerical scheme.
New explicit methods for the numerical solution of diffusion problems
Evans, David J.
In this survey paper, Part 1 is concerned with new explicit methods for the finite difference solution of a parabolic partial differential equation in 1 space dimension. The new methods use stable asymmetric approximations to the partial differential equation which when coupled in groups of 2 adjacent points on the grid result in implicit equations which can be easily converted to explicit form which in turn offer many advantages. By judicious use of alternating this strategy on the grid points of the domain results in an algorithm which possesses unconditional stability. Part II briefly surveys existing methods and then an explicit finite difference approximation procedure which is unconditionally stable for the solution of the two-dimensional nonhomogeneous diffusion equation is presented. This method possesses the advantages of the implicit methods, i.e., no severe limitation on the size of the time increment.
Numerical solutions of the complete Navier-Stokes equations
Hassan, H. A.
1993-01-01
The objective of this study is to compare the use of assumed pdf (probability density function) approaches for modeling supersonic turbulent reacting flowfields with the more elaborate approach where the pdf evolution equation is solved. Assumed pdf approaches for averaging the chemical source terms require modest increases in CPU time typically of the order of 20 percent above treating the source terms as 'laminar.' However, it is difficult to assume a form for these pdf's a priori that correctly mimics the behavior of the actual pdf governing the flow. Solving the evolution equation for the pdf is a theoretically sound approach, but because of the large dimensionality of this function, its solution requires a Monte Carlo method which is computationally expensive and slow to coverage. Preliminary results show both pdf approaches to yield similar solutions for the mean flow variables.
New Numerical Solution of von Karman Equation of Lengthwise Rolling
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Rudolf Pernis
2015-01-01
Full Text Available The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a by polygonal curve and (b by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. The new term relative stress as nondimensional variable was defined. The result from derived mathematical models can be calculated following variables: normal contact stress distribution, front and back tensions, angle of neutral point, coefficient of the arm of rolling force, rolling force, and rolling torque during rolling process. Laboratory cold rolled experiment of CuZn30 brass material was performed. Work hardening during brass processing was calculated. Comparison of theoretical values of normal contact stress with values of normal contact stress obtained from cold rolling experiment was performed. The calculations were not concluded with roll flattening.
Solution of simple numerical problems using spreadsheet programs
Riggi, F.
1986-11-01
Spreadsheet programs are now extensively used for the analysis of business problems. A spreadsheet program reproduces the structure of a large page with columns and rows. The intersection of a column and a row defines a cell, each cell being identified by a column letter and a row number, starting at the upper left. The screen is a window over this matrix, whose dimensions depend on the machine's resources. Unlike that which occurs with paper spreadsheets, the elements (cells) of such a matrix structure can hold not only labels or numerical values but also mathematical formulae relating them to other matrix elements.
Numerical solutions of Williamson fluid with pressure dependent viscosity
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Iffat Zehra
2015-01-01
Full Text Available In the present paper, we have examined the flow of Williamson fluid in an inclined channel with pressure dependent viscosity. The governing equations of motion for Williamson fluid model under the effects of pressure dependent viscosity and pressure dependent porosity are modeled and then solved numerically by the shooting method with Runge Kutta Fehlberg for two types of geometries i.e., (i Poiseuille flow and (ii Couette flow. Four different cases for pressure dependent viscosity and pressure dependent porosity are assumed and the physical features of pertinent parameters are discussed through graphs.
Numerical solution of two dimensional time fractional-order biological population model
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Prakash Amit
2016-01-01
Full Text Available In this work, we provide an approximate solution of a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model using a fractional variational iteration method (FVIM. Four test illustrations are used to show the proficiency and accuracy of the projected scheme. Comparisons between exact solutions and numerical solutions are presented for different values of fractional order α.
Vinci, C.; Renner, J.; Steeb, H.
2014-02-01
Characterization of subsurface fluid flow requires accounting for hydro-mechanical coupling between fluid-pressure variations and rock deformation. Particularly, flow of a compressible fluid along compliant hydraulic conduits, such as joints, fractures, or faults, is strongly affected by the associated deformation of the surrounding rock. We investigated and compared two alternative numerical modeling approaches that describe the transient fluid-pressure distribution along a single deformable fracture embedded in a rock matrix. First, we analyzed the coupled hydro-mechanical problem within the framework of Biot's poroelastic equations. Second, in a hybrid-dimensional approach, deformation characteristics of the surrounding rock were combined with a one-dimensional approximation of the fluid-flow problem to account for the high aspect ratios of fractures and the associated numerical problems. A dimensional analysis of the governing equations reveals that the occurring physical phenomena strongly depend on the geometry of the hydraulic conduit and on the boundary conditions. For the analyzed geometries, hydro-mechanical coupling effects dominate and convection effects can be neglected. Numerical solutions for coupled hydro-mechanical phenomena were obtained and compared to field data to characterize the fractured rock in the vicinity of an injection borehole. Either approach captures convection, diffusion, and hydro-mechanical effects, yet the hybrid-dimensional approach is advantageous due to its applicability to problems involving high-aspect-ratio features. For such cases, the modeling of pumping tests by means of the hybrid-dimensional approach showed that the observed inverse-pressure responses are the result of the coupling between the fluid flow in the fracture and the rock deformation caused by fluid-pressure variations along the fracture. Storage capacity as a single parameter of a fracture is insufficient to address all aspects of the coupling.
Semi-numerical solution for a fractal telegraphic dual-porosity fluid flow model
Herrera-Hernández, E C; Luis, D P; Hernández, D; Camacho-Velázquez, R G
2016-01-01
In this work, we present a semi-numerical solution of a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite difference method deals with the spatial coordinate. This semi-numerical scheme is not restricted by space discretization and allows the computation of a solution at any time without compromising numerical stability or the mass conservation principle. Our formulation results in a non-analytically-solvable second-order differential equation whose numerical treatment outcomes in a tri-diagonal linear algebraic system. Moreover, we describe comparisons between semi-numerical and semi-analytical solutions for particular cases. Results agree well with those from semi-analytic solutions. Furthermore, we expose a parametric analysis from the coupled model in order to show the effects of relevant parameters on pressure profiles and flow rates for the case where neither analytic nor sem...
The numerical solution of the vorticity transport equation
Dennis, S C R
1973-01-01
A method of approximating the two-dimensional vorticity transport equation in which the matrix associated with the difference equations is diagonally dominant and the truncation error is the same as that of the fully central-difference approximation, is discussed. An example from boundary layer theory is given by calculating the viscous stagnation point flow at the nose of a cylinder. Some new solutions of the Navier-Stokes equations are obtained for symmetrical flow past a flat plate of finite length. (16 refs).
A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
Trogdon, Thomas; Deconinck, Bernard
2014-01-01
In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t.
An Innovative Hybrid 3D Analytic-Numerical Approach for System Level Modelling of PEM Fuel Cells
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Gregor Tavčar
2013-10-01
Full Text Available The PEM fuel cell model presented in this paper is based on modelling species transport and coupling electrochemical reactions to species transport in an innovative way. Species transport is modelled by obtaining a 2D analytic solution for species concentration distribution in the plane perpendicular to the gas-flow and coupling consecutive 2D solutions by means of a 1D numerical gas-flow model. The 2D solution is devised on a jigsaw puzzle of multiple coupled domains which enables the modelling of parallel straight channel fuel cells with realistic geometries. Electrochemical and other nonlinear phenomena are coupled to the species transport by a routine that uses derivative approximation with prediction-iteration. A hybrid 3D analytic-numerical fuel cell model of a laboratory test fuel cell is presented and evaluated against a professional 3D computational fluid dynamic (CFD simulation tool. This comparative evaluation shows very good agreement between results of the presented model and those of the CFD simulation. Furthermore, high accuracy results are achieved at computational times short enough to be suitable for system level simulations. This computational efficiency is owed to the semi-analytic nature of its species transport modelling and to the efficient computational coupling of electrochemical kinetics and species transport.
Numerical solutions to the cosmological 3-fluid problem
Azreg-Aïnou, Mustapha
2013-12-01
We show that, for the scalar field cosmology with exponential potential, the set of values of the coupling parameter for which the solutions undergo a transient period of acceleration (TPA) is much larger than the set discussed in the literature. The gradual inclusion of ordinary and dark matters results in an everywhere, but near the origin, smoother and right shifted (along the time axis) acceleration curve. For the 3-fluid problem, the energy density need not exhibit a plateau during the acceleration period. Much excess in the dark matter and/or ordinary matter energy densities would lead the universe to undergo an eternal deceleration expansion. For the 3-fluid problem with a single exponential potential we conclude that the Big Bang Nucleosynthesis constraint is not fulfilled if the universe is to undergo a TPA. The 3-fluid model remains a good approximation for the description of large scale structures.
Symmetry preserving compact schemes for numerical solution of PDEs
Ozbenli, Ersin; Vedula, Prakash
2017-11-01
In this study, a new approach for construction of invariant, high order accurate compact finite difference schemes that preserve Lie symmetry groups of underlying partial differential equations (PDEs) is presented. It is well known that compact numerical schemes based on Pade approximants achieve high order accuracy with a relatively small number of stencil points and are found to have good spectral-like resolution. Considering applicable Lie symmetry groups (such as translation, scaling, rotation, and projection groups) of underlying PDEs, invariant compact schemes are developed based on the use of equivariant moving frames and extended group transformations. This work represents an extension of the authors recent work on construction of invariant, high-order, non-compact, finite difference schemes based on the method of modified equations. Performance of the proposed symmetry preserving compact schemes is evaluated via consideration of some canonical PDEs like linear advection-diffusion equation, inviscid Burgers' equation, and viscous Burgers' equation. Effects on accuracy due to choice of subgroups used in construction of these schemes will be discussed. Generalization of the proposed framework to multidimensional problems and non-orthogonal grids will also be presented.
Experimental and Numerical Characterization of a Hybrid Fabry-Pérot Cavity for Temperature Sensing
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Aitor Lopez-Aldaba
2015-04-01
Full Text Available A hybrid Fabry-Pérot cavity sensing head based on a four-bridge microstructured fiber is characterized for temperature sensing. The characterization of this cavity is performed numerically and experimentally in the L-band. The sensing head output signal presents a linear variation with temperature changes, showing a sensitivity of 12.5 pm/°C. Moreover, this Fabry-Pérot cavity exhibits good sensitivity to polarization changes and high stability over time.
Gómez-Aguilar, J. F.
2018-03-01
In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.
Chiu, Min-Chie
2013-06-01
A broadband noise hybridized with pure tones often occurs in practical engineering work. However, assessments of a muffler's optimal shape design that would simultaneously overcome a broadband noise hybridized with multiple tones within a constrained space were rarely addressed. In order to promote the best acoustical performance in mufflers, five kinds of the hybrid mufflers composed of a reactive unit, a dissipative unit, and Helmholtz resonator (HR) units will be proposed. Moreover, to strengthen the noise elimination at the pure tone, mufflers having parallel multiple-sectioned HRs or having multiple HR connections in series (muffler D and muffler E) will be also presented in the noise abatement. On the basis of the plane wave theory, the four-pole system matrix used to evaluate the acoustic performance of a multi-tone hybrid Helmholtz muffler will be presented. A numerical case for eliminating broadband noise hybridized with a pure tone emitted from a machine room using five kinds of mufflers (muffler A-E) will also be introduced. To find the best acoustical performance of a space-constrained muffler, a numerical assessment using a simulated annealing (SA) method is adopted. To verify the availability of the SA optimization, a numerical optimization of muffler A at a pure tone (280 Hz) is exemplified. Before the SA operation can be carried out, the accuracy of the mathematical model will be checked using the experimental data. The influences of the sound transmission loss (STL) with respect to N1-array HR and the STL with respect to one-array HR sectioned in N2 divisions have also been assessed. Also, the influence of the STL with respect to the design parameters such as the ratio of d1/d2, the diameter of the perforated hole (dH), the porosity (p%) of the perforated plate, and the outer diameter (d2) of the dissipative unit has been analyzed. Consequently, a successful approach in eliminating a broadband noise hybridized with a pure tone using optimally
Numerical solution of the Fokker--Planck equations for a multi-species plasma
Energy Technology Data Exchange (ETDEWEB)
Killeen, J.; Mirin, A.A.
1977-03-11
Two numerical models used for studying collisional multispecies plasmas are described. The mathematical model is the Boltzmann kinetic equation with Fokker-Planck collision terms. A one-dimensional code and a two-dimensional code, used for the solution of the time-dependent Fokker-Planck equations for ion and electron distribution functions in velocity space, are described. The required equations and boundary conditions are derived and numerical techniques for their solution are given.
Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind
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Abdon Atangana
2013-01-01
Full Text Available This work presents the possible generalization of the Volterra integral equation second kind to the concept of fractional integral. Using the Picard method, we present the existence and the uniqueness of the solution of the generalized integral equation. The numerical solution is obtained via the Simpson 3/8 rule method. The convergence of this scheme is presented together with numerical results.
Organic-inorganic hybrid solution-processed H2-evolving photocathodes
Lai, L.H.; Gomulya, W.; Berghuis, M.; Protesescu, L.; Detz, R.J.; Reek, J.N.H.; Kovalenko, M.V.; Loi, M.A.
2015-01-01
Here we report for the first time an H2-evolving photocathode fabricated by a solution-processed organic inorganic hybrid composed of CdSe and P3HT. The CdSe:P3HT (10:1 (w/w)) hybrid bulk heterojunction treated with 1,2-ethanedithiol (EDT) showed efficient water reduction and hydrogen generation. A
Organic-Inorganic Hybrid Solution-Processed H-2-Evolving Photocathodes
Lai, Lai-Hung; Gomulya, Widianta; Berghuis, Matthijs; Protesescu, Loredana; Detz, Remko J.; Reek, Joost N. H.; Kovalenko, Maksym V.; Loi, Maria A.
2015-01-01
Here we report for the first time an H-2-evolving photocathode fabricated by a solution-processed organic inorganic hybrid composed of CdSe and P3HT. The CdSe:P3HT (10:1 (w/w)) hybrid bulk heterojunction treated with 1,2-ethanedithiol (EDT) showed efficient water reduction and hydrogen generation. A
Numerical solution of two-dimensional non-linear partial differential ...
African Journals Online (AJOL)
differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be solved at each time level. To linearize the resulting system of difference equations, Newton ...
Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil
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Kryštůfek P.
2014-03-01
Full Text Available The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
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De-Gang Wang
2012-01-01
Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.
Numerical Solution of Compressible Steady Flows around the NACA 0012 Airfoil
Kozel K.; Kryštůfek P.
2013-01-01
The article presents results of a numerical solution of subsonic and transonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the NACA 0012 airfoil. Authors used Runge-Kutta method to numerically solve the flows around the NACA 0012 airfoil.
A numerical solution for a class of time fractional diffusion equations with delay
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Pimenov Vladimir G.
2017-09-01
Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
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Grégory Antoni
2017-01-01
Full Text Available The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.
Yıgıt, Gülsemay; Bayram, Mustafa
2017-01-01
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient matrix which is necessary to get numerical results. Following this, different class of perturbation problems are considered as test problems. Then, all results are shown in tables and also comparison between numerical and exact solution shows the accuracy a...
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John F. Moxnes
2014-06-01
Full Text Available There has been increasing interest in numerical simulations of fragmentation of expanding warheads in 3D. Accordingly there is a pressure on developers of leading commercial codes, such as LS-DYNA, AUTODYN and IMPETUS Afea, to implement the reliable fracture models and the efficient solution techniques. The applicability of the Johnson–Cook strength and fracture model is evaluated by comparing the fracture behaviour of an expanding steel casing of a warhead with experiments. The numerical codes and different numerical solution techniques, such as Eulerian, Lagrangian, Smooth particle hydrodynamics (SPH, and the corpuscular models recently implemented in IMPETUS Afea are compared. For the same solution techniques and material models we find that the codes give similar results. The SPH technique and the corpuscular technique are superior to the Eulerian technique and the Lagrangian technique (with erosion when it is applied to materials that have fluid like behaviour such as the explosive and the tracer. The Eulerian technique gives much larger calculation time and both the Lagrangian and Eulerian techniques seem to give less agreement with our measurements. To more correctly simulate the fracture behaviours of the expanding steel casing, we applied that ductility decreases with strain rate. The phenomena may be explained by the realization of adiabatic shear bands. An implemented node splitting algorithm in IMPETUS Afea seems very promising.
Numerical solution of first order initial value problem using quartic spline method
Ala'yed, Osama; Ying, Teh Yuan; Saaban, Azizan
2015-12-01
Any first order initial value problem can be integrated numerically by discretizing the interval of integration into a number of subintervals, either with equally distributed grid points or non-equally distributed grid points. Hence, as the integration advances, the numerical solutions at the grid points are calculated and being known. However, the numerical solutions between the grid points remain unknown. This will form difficulty to individuals who wish to study a particular solution which may not fall on the grid points. Therefore, some sorts of interpolation techniques are needed to deal with such difficulty. Spline interpolation technique remains as a well known approach to approximate the numerical solution of a first order initial value problem, not only at the grid points but also everywhere between the grid points. In this short article, a new quartic spline method has been derived to obtain the numerical solution for first order initial value problem. The key idea of the derivation is to treat the third derivative of the quartic spline function to be a linear polynomial, and obtain the quartic spline function with undetermined coefficients after three integrations. The new quartic spline function is ready to be used when all unknown coefficients are found. We also described an algorithm for the new quartic spline method when used to obtain the numerical solution of any first order initial value problem. Two test problems have been used for numerical experimentations purposes. Numerical results seem to indicate that the new quartic spline method is reliable in solving first order initial value problem. We have compared the numerical results generated by the new quartic spline method with those obtained from an existing spline method. Both methods are found to have comparable accuracy.
Numerical solutions of a three-point boundary value problem with an ...
African Journals Online (AJOL)
Numerical solutions of a three-point boundary value problem with an integral condition for a third-order partial differential equation by using Laplace transform method Solutions numeriques d'un probleme pour une classe d'equations differentielles d'ordr.
Numerical Solution of Quantum Cosmological Model Simulating Boson and Fermion Creation
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Christianto V.
2009-04-01
Full Text Available A numerical solution of Wheeler-De Witt equation for a quantum cosmological model simulating boson and fermion creation in the early Universe evolution is presented. This solution is based on a Wheeler-De Witt equation obtained by Krechet, Fil’chenkov, and Shikin, in the framework of quantum geometrodynamics for a Bianchi-I metric.
Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method
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Limei Yan
2013-01-01
Full Text Available A relatively new iterative Laplace transform method, which combines two methods; the iterative method and the Laplace transform method, is applied to obtain the numerical solutions of fractional Fokker-Planck equations. The method gives numerical solutions in the form of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and straightforward when applied to space-time fractional Fokker-Planck equations. The method provides a promising tool for solving space-time fractional partial differential equations.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver.
Cisneros, L. A.; Ize, J.; Minzoni, A. A.
2009-07-01
We develop a modulation theory based on a suitably averaged Lagrangian for steady solutions of the Sine-Gordon equation in a two dimensional lattice. These lump solutions are nonzero in circular or polygonal regions and zero elsewhere. The modulation theory gives approximate solutions away from small perturbations of the exact anti-continuum solutions for both radial and polygonal solutions. We show how the Peierls-Nabarro potential determines the shape of the boundary between excited sites and the zero solution. These solutions are compared with the corresponding numerical solutions and significant agreement is found. Moreover, we show that solutions with a large radius (more than sixteen lattice sites) can be explained using a continuous trial function for the averaged Lagrangian, while smaller polygonal solutions can be constructed using a trial function, which takes into account the angular variation of the boundary imposed by the lattice. Finally, the ideas of equivariant bifurcation theory are used to obtain a full numerical description of the solution branches as functions of the coupling parameter between neighboring sites. The results of this work can be used to study steady solutions for other types of lattice equations.
Tavčar, Gregor; Katrašnik, Tomaž
2014-01-01
The parallel straight channel PEM fuel cell model presented in this paper extends the innovative hybrid 3D analytic-numerical (HAN) approach previously published by the authors with capabilities to address ternary diffusion systems and counter-flow configurations. The model's core principle is modelling species transport by obtaining a 2D analytic solution for species concentration distribution in the plane perpendicular to the cannel gas-flow and coupling consecutive 2D solutions by means of a 1D numerical pipe-flow model. Electrochemical and other nonlinear phenomena are coupled to the species transport by a routine that uses derivative approximation with prediction-iteration. The latter is also the core of the counter-flow computation algorithm. A HAN model of a laboratory test fuel cell is presented and evaluated against a professional 3D CFD simulation tool showing very good agreement between results of the presented model and those of the CFD simulation. Furthermore, high accuracy results are achieved at moderate computational times, which is owed to the semi-analytic nature and to the efficient computational coupling of electrochemical kinetics and species transport.
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Handlovičová Angela
2016-01-01
Full Text Available In this paper, the numerical solution to the Helmholtz equation with impedance boundary condition, based on the Finite volume method, is discussed. We used the Robin boundary condition using exterior points. Properties of the weak solution to the Helmholtz equation and numerical solution are presented. Further the numerical experiments, comparing the numerical solution with the exact one, and the computation of the experimental order of convergence are presented.
Wang, Jinting; Lu, Liqiao; Zhu, Fei
2018-01-01
Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.
Energy Technology Data Exchange (ETDEWEB)
Loch, Guilherme G.; Bevilacqua, Joyce S., E-mail: guiloch@ime.usp.br, E-mail: joyce@ime.usp.br [Universidade de Sao Paulo (IME/USP), Sao Paulo, SP (Brazil). Departamento de Matematica Aplicada. Instituto de Matematica e Estatistica; Hiromoto, Goro; Rodrigues Junior, Orlando, E-mail: rodrijr@ipen.br, E-mail: hiromoto@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN-CNEN/SP), Sao Paulo, SP (Brazil)
2013-07-01
The implementation of stable and efficient numerical methods for solving problems involving nuclear transmutation and radioactive decay chains is the main scope of this work. The physical processes associated with irradiations of samples in particle accelerators, or the burning spent nuclear fuel in reactors, or simply the natural decay chains, can be represented by a set of first order ordinary differential equations with constant coefficients, for instance, the decay radioactive constants of each nuclide in the chain. Bateman proposed an analytical solution for a particular case of a linear chain with n nuclides decaying in series and with different decay constants. For more complex and realistic applications, the construction of analytical solutions is not viable and the introduction of numerical techniques is imperative. However, depending on the magnitudes of the decay radioactive constants, the matrix of coefficients could be almost singular, generating unstable and non convergent numerical solutions. In this work, different numerical strategies for solving systems of differential equations were implemented, the Runge-Kutta 4-4, Adams Predictor-Corrector (PC2) and the Rosenbrock algorithm, this last one more specific for stiff equations. Consistency, convergence and stability of the numerical solutions are studied and the performance of the methods is analyzed for the case of the natural decay chain of Uranium-235 comparing numerical with analytical solutions. (author)
A numerical guide to the solution of the bidomain equations of cardiac electrophysiology
Pathmanathan, Pras
2010-06-01
Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.
Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions
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R. Jooma
2017-01-01
Full Text Available A time dependent nonlinear partial differential equation modelling heat transfer in a porous radial fin is considered. The Differential Transformation Method is employed in order to account for the steady state case. These solutions are then used as a means of assessing the validity of the numerical solutions obtained via the Crank-Nicolson finite difference method. In order to engage in the stability of this scheme we conduct a stability and dynamical systems analysis. These provide us with an assessment of the impact of the nonlinear sink terms on the stability of the numerical scheme employed and on the dynamics of the solutions.
Numerical Study on Couette Flow in Nanostructured Channel using Molecular-continuum Hybrid Method
Energy Technology Data Exchange (ETDEWEB)
Kim, Youngjin; Jeong, Myunggeun; Ha, Man Yeong [Pusan Nat’l Univ., Busan (Korea, Republic of)
2017-06-15
A molecular-continuum hybrid method was developed to simulate microscale and nanoscale fluids where continuum fluidic cannot be used to predict Couette flow. Molecular dynamics simulation is used near the solid surface where the flow cannot be predicted by continuum fluidic, and Navier-Stokes equations are used in the other regions. Numerical simulation of Couette flow was performed using the hybrid method to investigate the effect of solid-liquid interaction and surface roughness in a nanochannel. It was found that the solid-liquid interaction and surface roughness influence the boundary condition. When the surface energy is low, slippage occurs near the solid surface, and the magnitude of slippage decreases with increase in surface energy. When the surface energy is high, a locking boundary condition is formed. The roughness disturbs slippage near the solid surface and promotes the locking boundary condition.
A New Hybrid MGBPSO-GSA Variant for Improving Function Optimization Solution in Search Space
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Narinder Singh
2017-03-01
Full Text Available In this article, a newly hybrid nature-inspired approach (MGBPSO-GSA is developed with a combination of Mean Gbest Particle Swarm Optimization (MGBPSO and Gravitational Search Algorithm (GSA. The basic inspiration is to integrate the ability of exploitation in MGBPSO with the ability of exploration in GSA to synthesize the strength of both approaches. As a result, the presented approach has the automatic balance capability between local and global searching abilities. The performance of the hybrid approach is tested on a variety of classical functions, ie, unimodal, multimodal, and fixed-dimension multimodal functions. Furthermore, Iris data set, Heart data set, and economic dispatch problems are used to compare the hybrid approach with several metaheuristics. Experimental statistical solutions prove empirically that the new hybrid approach outperforms significantly a number of metaheuristics in terms of solution stability, solution quality, capability of local and global optimum, and convergence speed.
A New Hybrid MGBPSO-GSA Variant for Improving Function Optimization Solution in Search Space.
Singh, Narinder; Singh, Sharandeep; Singh, S B
2017-01-01
In this article, a newly hybrid nature-inspired approach (MGBPSO-GSA) is developed with a combination of Mean Gbest Particle Swarm Optimization (MGBPSO) and Gravitational Search Algorithm (GSA). The basic inspiration is to integrate the ability of exploitation in MGBPSO with the ability of exploration in GSA to synthesize the strength of both approaches. As a result, the presented approach has the automatic balance capability between local and global searching abilities. The performance of the hybrid approach is tested on a variety of classical functions, ie, unimodal, multimodal, and fixed-dimension multimodal functions. Furthermore, Iris data set, Heart data set, and economic dispatch problems are used to compare the hybrid approach with several metaheuristics. Experimental statistical solutions prove empirically that the new hybrid approach outperforms significantly a number of metaheuristics in terms of solution stability, solution quality, capability of local and global optimum, and convergence speed.
A New Hybrid MGBPSO-GSA Variant for Improving Function Optimization Solution in Search Space
Singh, Narinder; Singh, Sharandeep; Singh, S B
2017-01-01
In this article, a newly hybrid nature-inspired approach (MGBPSO-GSA) is developed with a combination of Mean Gbest Particle Swarm Optimization (MGBPSO) and Gravitational Search Algorithm (GSA). The basic inspiration is to integrate the ability of exploitation in MGBPSO with the ability of exploration in GSA to synthesize the strength of both approaches. As a result, the presented approach has the automatic balance capability between local and global searching abilities. The performance of the hybrid approach is tested on a variety of classical functions, ie, unimodal, multimodal, and fixed-dimension multimodal functions. Furthermore, Iris data set, Heart data set, and economic dispatch problems are used to compare the hybrid approach with several metaheuristics. Experimental statistical solutions prove empirically that the new hybrid approach outperforms significantly a number of metaheuristics in terms of solution stability, solution quality, capability of local and global optimum, and convergence speed. PMID:28469380
Numerical investigation on the regression rate of hybrid rocket motor with star swirl fuel grain
Zhang, Shuai; Hu, Fan; Zhang, Weihua
2016-10-01
Although hybrid rocket motor is prospected to have distinct advantages over liquid and solid rocket motor, low regression rate and insufficient efficiency are two major disadvantages which have prevented it from being commercially viable. In recent years, complex fuel grain configurations are attractive in overcoming the disadvantages with the help of Rapid Prototyping technology. In this work, an attempt has been made to numerically investigate the flow field characteristics and local regression rate distribution inside the hybrid rocket motor with complex star swirl grain. A propellant combination with GOX and HTPB has been chosen. The numerical model is established based on the three dimensional Navier-Stokes equations with turbulence, combustion, and coupled gas/solid phase formulations. The calculated fuel regression rate is compared with the experimental data to validate the accuracy of numerical model. The results indicate that, comparing the star swirl grain with the tube grain under the conditions of the same port area and the same grain length, the burning surface area rises about 200%, the spatially averaged regression rate rises as high as about 60%, and the oxidizer can combust sufficiently due to the big vortex around the axis in the aft-mixing chamber. The combustion efficiency of star swirl grain is better and more stable than that of tube grain.
Directory of Open Access Journals (Sweden)
V. M. Mikhailov
2017-12-01
Full Text Available Purpose. Testing of numerical solution algorithm for integral equation for calculation of plane meridian magnetostatic field source distribution at interfaces of piecewise homogeneous magnetized medium by means of electrostatic analogy. Methodology. The piecewise homogeneous medium consists of three regions with different magnetic permeabilities: the shell of arbitrary meridian section, external unlimited medium outside the shell, and the medium inside the shell. For testing external homogeneous magnetic field effect on spherical shell is considered. The analytical solution of this problem on the basis of electrostatic analogy from the solution of the problem uniform electrostatic field effect on dielectric shell is obtained. We have compared results of numerical solution of integral equation with the data obtained by means of analytical solution at the variation of magnetic permeabilities of regions of medium. Results. Integral equation and the algorithm of its numerical solution for calculation of source field distribution at the boundaries of piecewise homogeneous medium is validated. Testing of integral equations correctness for calculation of fictitious magnetic charges distribution on axisymmetric boundaries of piecewise homogeneous magnetized medium and algorithms of their numerical solutions can be carried out by means of analytical solutions of problems of homogeneous electrostatic field effect analysis on piecewise homogeneous dielectric medium with central symmetry of boundaries – single-layer and multilayer spherical shells. In the case of spherical shell in wide range of values of the parameter λk, including close to ± 1, numerical solution of integral equation is stable, and relative error in calculating of fictitious magnetic charges surface density and magnetic field intensity inside the shell is from tenths of a percent up to several percent except for the cases of very small values of these quantities. Originality. The use
Liu, Junsheng; Ma, Yue; Zhang, Yaping; Shao, Guoquan
2010-01-15
Using zwitterionic hybrid polymers as adsorbent, the adsorption kinetics and isotherm, thermodynamic parameters of Delta G, Delta H and DeltaS for the removal of Pb(2+) from aqueous solution were investigated. It is indicated that the adsorption of Pb(2+) ions on these zwitterionic hybrid polymers followed the Lagergren second-order kinetic model and Freundlich isotherm model, demonstrating that the adsorption process might be Langmuir monolayer adsorption. The negative values of Delta G and the positive values of Delta H evidence that Pb(2+) adsorption on these zwitterionic hybrid polymers is spontaneous and endothermic process in nature. Moreover, the zwitterionic hybrid polymers produced reveal relatively higher desorption efficiency in 2 mol dm(-3) aqueous HNO(3) solution, indicating that they can be recycled in industrial processes. These findings suggest that these zwitterionic hybrid polymers are the promising adsorbents for Pb(2+) removal and can be potentially applied in the separation and recovery of Pb(2+) ions from the waste chemicals and contaminated water of lead-acid rechargeable battery.
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Mark A Lau
2016-09-01
Full Text Available This paper presents the implementation of numerical and analytical solutions of some of the classical partial differential equations using Excel spreadsheets. In particular, the heat equation, wave equation, and Laplace’s equation are presented herein since these equations have well known analytical solutions. The numerical solutions can be easily obtained once the differential equations are discretized via finite differences and then using cell formulas to implement the resulting recursive algorithms and other iterative methods such as the successive over-relaxation (SOR method. The graphing capabilities of spreadsheets can be exploited to enhance the visualization of the solutions to these equations. Furthermore, using Visual Basic for Applications (VBA can greatly facilitate the implementation of the analytical solutions to these equations, and in the process, one obtains Fourier series approximations to functions governing initial and/or boundary conditions.
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Li Mao
2016-01-01
Full Text Available Artificial bee colony (ABC algorithm has good performance in discovering the optimal solutions to difficult optimization problems, but it has weak local search ability and easily plunges into local optimum. In this paper, we introduce the chemotactic behavior of Bacterial Foraging Optimization into employed bees and adopt the principle of moving the particles toward the best solutions in the particle swarm optimization to improve the global search ability of onlooker bees and gain a hybrid artificial bee colony (HABC algorithm. To obtain a global optimal solution efficiently, we make HABC algorithm converge rapidly in the early stages of the search process, and the search range contracts dynamically during the late stages. Our experimental results on 16 benchmark functions of CEC 2014 show that HABC achieves significant improvement at accuracy and convergence rate, compared with the standard ABC, best-so-far ABC, directed ABC, Gaussian ABC, improved ABC, and memetic ABC algorithms.
Numerical Simulation of Carbon Nanotubes/GaAs Hybrid PV Devices with AMPS-1D
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Georgi Xosrovashvili
2014-01-01
Full Text Available The performance and characteristics of a hybrid heterojunction single-walled carbon nanotube and GaAs solar cell are modelled and numerically simulated using AMPS-1D device simulation tool. The device physics and performance with different junction parameters are analysed. The results suggest that the open-circuit voltage changes very slightly by changing the electron affinity, acceptor and donor density while the other electrical parameters reach an optimum value. Increasing the concentration of a discrete defect density in the absorber layer decreases the electrical parameters. The current-voltage characteristics, quantum efficiency, band gap, and thickness variation of the photovoltaic response will be quantitatively considered.
Three-Step Hybrid Linear Multistep Method for Solution of First ...
African Journals Online (AJOL)
In this article, a three-step hybrid linear multistep method for solution of first order initial value problems (IVPs) in ordinary differential differential equations (ODEs) is proposed. Essentially, the method is based on collocation of the differential system and the interpolation of the approximate solution at the grid and off-grid ...
DEFF Research Database (Denmark)
Barrera Figueroa, Salvador; Rasmussen, Knud; Jacobsen, Finn
2009-01-01
Typically, numerical calculations of the pressure, free-field, and random-incidence response of a condenser microphone are carried out on the basis of an assumed displacement distribution of the diaphragm of the microphone; the conventional assumption is that the displacement follows a Bessel...... to this problem is to measure the velocity distribution of the membrane by means of a non-contact method, such as laser vibrometry. The measured velocity distribution can be used together with a numerical formulation such as the boundary element method for estimating the microphone response and other parameters......, e.g., the acoustic center. In this work, such a hybrid method is presented and examined. The velocity distributions of a number of condenser microphones have been determined using a laser vibrometer, and these measured velocity distributions have been used for estimating microphone responses...
Modelling of blast-induced damage in tunnels using a hybrid finite-discrete numerical approach
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Amichai Mitelman
2014-12-01
Full Text Available This paper presents the application of a hybrid finite-discrete element method to study blast-induced damage in circular tunnels. An extensive database of field tests of underground explosions above tunnels is used for calibrating and validating the proposed numerical method; the numerical results are shown to be in good agreement with published data for large-scale physical experiments. The method is then used to investigate the influence of rock strength properties on tunnel durability to withstand blast loads. The presented analysis considers blast damage in tunnels excavated through relatively weak (sandstone and strong (granite rock materials. It was found that higher rock strength will increase the tunnel resistance to the load on one hand, but decrease attenuation on the other hand. Thus, under certain conditions, results for weak and strong rock masses are similar.
Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem
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Susmita Paul
2016-01-01
Full Text Available We try to compare the solutions by some numerical techniques when we apply the methods on some mathematical biology problems. The Runge-Kutta-Fehlberg (RKF method is a promising method to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for insect population, one-species Lotka-Volterra model. The technique is described and illustrated by numerical examples. We modify the population models by taking the Holling type III functional response and intraspecific competition term and hence we solve it by this numerical technique and show that RKF method gives good results. We try to compare this method with the Laplace Adomian Decomposition Method (LADM and with the exact solutions.
Smoluchowski aggregation-fragmentation equations: Fast numerical algorithm for steady-state solution
Stadnichuk, Vladimir; Bodrova, Anna; Brilliantov, Nikolai
2015-01-01
We propose an efficient and fast numerical algorithm of finding a \\emph{stationary} solution of large systems of aggregation-fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable when the stationary concentrations steeply decreases with increasing aggregate size, which is fulfilled for the most important cases. We show that under rather mild restrictions, imposed on the kernel of the Smoluchowski equation, the following numerical proc...
Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline
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Ravi Kanth A.S.V.
2016-01-01
Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.
Numerical solutions of multi-order fractional differential equations by Boubaker polynomials
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Bolandtalat A.
2016-01-01
Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.
Oscillating solutions of the Vlasov-Poisson system-A numerical investigation
Ramming, Tobias; Rein, Gerhard
2018-02-01
Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in time or damped. Along one-parameter families of polytropic steady states we establish an Eddington-Ritter type relation which relates the period of the oscillation to the central density of the steady state. The numerically obtained periods are used to estimate possible periods for typical elliptical galaxies.
Numerical Solution of The Linear Fredholm Integral Equations of the Second Kind
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N. Parandin
2010-03-01
Full Text Available The theory of integral equation is one of the major topics of applied mathematics. The main purpose of this paper is to introduce a numerical method based on the interpolation for approximating the solution of the second kind linear Fredholm integral equation. In this case, the divided differences method is applied. At last, two numerical examples are presented to show the accuracy of the proposed method
Higher-order numerical solutions using cubic splines. [for partial differential equations
Rubin, S. G.; Khosla, P. K.
1975-01-01
A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-
2nd International Workshop on the Numerical Solution of Markov Chains
1995-01-01
Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.
Nacozy, P. E.
1984-01-01
The equations of motion are developed for a perfectly flexible, inelastic tether with a satellite at its extremity. The tether is attached to a space vehicle in orbit. The tether is allowed to possess electrical conductivity. A numerical solution algorithm to provide the motion of the tether and satellite system is presented. The resulting differential equations can be solved by various existing standard numerical integration computer programs. The resulting differential equations allow the introduction of approximations that can lead to analytical, approximate general solutions. The differential equations allow more dynamical insight of the motion.
Solutions manual to accompany An introduction to numerical methods and analysis
Epperson, James F
2014-01-01
A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp
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Sankalap Arora
2017-08-01
Full Text Available In this paper, a new hybrid optimization algorithm which combines the standard Butterfly Optimization Algorithm (BOA with Artificial Bee Colony (ABC algorithm is proposed. The proposed algorithm used the advantages of both the algorithms in order to balance the trade-off between exploration and exploitation. Experiments have been conducted on the proposed algorithm using ten benchmark problems having a broad range of dimensions and diverse complexities. The simulation results demonstrate that the convergence speed and accuracy of the proposed algorithm in finding optimal solutions is significantly better than BOA and ABC.
A Mathematical and Numerical Model for the Analysis of Hybrid Rocket Motors
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Florin MINGIREANU
2011-12-01
Full Text Available The hybrid rocket motors (HRM use a two-phase propellant system. This offers some remarkable advantages but also arises some difficulties like the neutralization of their instabilities. The non-acoustic combustion instabilities are high-amplitude pressure oscillations that have too low frequencies to be associated with acoustics. Acoustic type combustion instabilities are self-excited oscillations generated by the interaction between acoustic waves and combustion. The goal of the present work is to develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. This model must be useful for transient and stability analysis and also for scaling of HRMs. The numerical results obtained with our model show a good agreement with published experimental and numerical results. The computational and stability analysis models developed in this work are simple, computationally efficient and offer the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.
Numerical research of hydrodynamic performance of hybrid CRP podded propulsor in steering conditions
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XU Jiaqi
2017-03-01
Full Text Available In order to study the influence of steering conditions to hybrid CRP podded propulsor,the calculation of the NACA0012 open-water rudder's lift coefficient was carried out by applying the RANS method combined with the SST k-ω turbulence model, and the near wall mesh arrangement and near wall treatment method applied in numerical calculation were selected through comparisons between the experimental results and the calculation results. The hydrodynamic performance of a podded propulsor was predicted on the basis of the above, and the calculation results showed a good agreement with the experimental results. The object of the research was a hybrid CRP podded propulsor, and its hydrodynamic performance in steering conditions was predicted by applying the numerical method above. Conclusions were drawn on the relationship between hydrodynamic performance parameters and steering angle, i.e. larger magnitudes of the after propeller thrust, pod horizontal force and steering moment will be acquired at larger steering angles, and the fore propeller thrust is basically as invariant as the pod steering. The internal reasons were also analyzed. Research shows that the propeller has good maneuverability,and will have wide application prospect.
Use of Green's functions in the numerical solution of two-point boundary value problems
Gallaher, L. J.; Perlin, I. E.
1974-01-01
This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.
Two different methods for numerical solution of the modified Burgers' equation.
Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi
2014-01-01
A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM.
Finite analytic numerical solution of two-dimensional channel flow over a backward-facing step
Ho, K.-S.; Chen, C.-J.
1986-01-01
Laminar channel flow over a backward-facing step is investigated. The finite analytic (FA) method is used to obtain the numerical solution. The FA solutions predict the recirculation zone lengths and the recirculated mass flow rates for Reynolds numbers, Re, of 25, 50, 73, 125, 191 and 229 which correlate well with experimental measurements. The general flow patterns of the recirculation region flows for the Reynolds numbers considered in this study are similar to each other.
Yang, Xiaohui
2012-01-01
Traditional materials for application in organic light emitting diodes (OLEDs) are primarily based on small molecules and polymers, with much fewer examples of intermediate molecular weight materials. Our interest lies in this intermediate molecular weight range, specifically in hybrids based on 3-dimensional silsesquioxane (SSQ) cores that represents a new class of versatile materials for application in solution processable OLEDs. We report here various SSQ based hybrids that are easily prepared in one high-yield step from the Heck coupling of commercially available 1-bromopyrene, and 1-bromo-4-heptylbenzene with octavinyl-T8-SSQ, and a mixture of octavinyl-T8-, decavinyl-T10- and dodecavinyl-T12-SSQ. The resulting materials offer numerous advantages for OLEDs including amorphous properties, high-glass-transition temperatures (T g), low polydispersity, solubility in common solvents, and high purity via column chromatography. Solution processed OLEDs prepared from the SSQ hybrids provide sky-blue emission with external quantum efficiencies and current efficiencies of 3.64% and 9.56 cd A -1 respectively. © 2012 The Royal Society of Chemistry.
A Hybrid Numerical Method for Turbulent Mixing Layers. Degree awarded by Case Western Reserve Univ.
Georgiadis, Nicholas J.
2001-01-01
A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modern day aircraft and also those of hypersonic vehicles currently under development. The method configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. Closure for the RANS equations was obtained using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The wall-function approach enabled a continuous computational grid from the RANS regions to the LES region. The LES equations were closed using the Smagorinsky subgrid scale model. The hybrid RANS-LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Vortex shedding from the base region of a splitter plate separating the upstream flows was observed to eventually transition to turbulence. The location of the transition, however, was much further downstream than indicated by experiments. Actual LES calculations, performed in three spatial directions, also indicated vortex shedding, but the transition to turbulence was found to occur much closer to the beginning of the mixing section. which is in agreement with experimental observations. These calculations demonstrated that LES simulations must be performed in three dimensions. Comparisons of time-averaged axial velocities and turbulence intensities indicated reasonable agreement with experimental
Analytical solutions and numerical modeling for a dam-break problem in inclined channels
Pelinovsky, Efim; Didenkulova, Ira; Didenkulov, Oleg; Rodin, Artem
2016-04-01
Here we obtain different analytical solutions of the shallow-water equations for inviscid nonlinear waves in inclined channels. (i) The first solution describes Riemann wave moving up or down alone the channel slope. It requires the initial fluid flow, which often accompanies waves generated by landslides. This solution is valid for a finite time before the wave breaks. (ii) The second solution generalizes the classical dam-break problem for the case of a dam located in the inclined channel. In this case the cross-section of the channel influences the speed of wave propagation inside the channel, and therefore changes wave dynamics inside the channel compare to the plane beach. (iii) The third solution describes the intermediate stage of the wave front dynamics for a dam of a large height. This solution is derived with the use of generalized Carrier-Greenspan approach developed early by Didenkulova & Pelinovsky (2011) and Rybkin et al (2014). Some of the analytical solutions are tested with the means of numerical modeling. The numerical modeling is carried out using the CLAWPACK software based on nonlinear shallow water equations. Application of the described solutions to possible laboratory experiments is discussed.
On the limits of numerical astronomical solutions used in paleoclimate studies
Zeebe, Richard E.
2017-04-01
Numerical solutions of the equations of the Solar System estimate Earth's orbital parameters in the past and represent the backbone of cyclostratigraphy and astrochronology, now widely applied in geology and paleoclimatology. Given one numerical realization of a Solar System model (i.e., obtained using one code or integrator package), various parameters determine the properties of the solution and usually limit its validity to a certain time period. Such limitations are denoted here as "internal" and include limitations due to (i) the underlying physics/physical model and (ii) numerics. The physics include initial coordinates and velocities of Solar System bodies, treatment of the Moon and asteroids, the Sun's quadrupole moment, and the intrinsic dynamics of the Solar System itself, i.e., its chaotic nature. Numerical issues include solver algorithm, numerical accuracy (e.g., time step), and round-off errors. At present, internal limitations seem to restrict the validity of astronomical solutions to perhaps the past 50 or 60 myr. However, little is currently known about "external" limitations, that is, how do different numerical realizations compare, say, between different investigators using different codes and integrators? Hitherto only two solutions for Earth's eccentricity appear to be used in paleoclimate studies, provided by two different groups that integrated the full Solar System equations over the past >100 myr (Laskar and coworkers and Varadi et al. 2003). In this contribution, I will present results from new Solar System integrations for Earth's eccentricity obtained using the integrator package HNBody (Rauch and Hamilton 2002). I will discuss the various internal limitations listed above within the framework of the present simulations. I will also compare the results to the existing solutions, the details of which are still being sorted out as several simulations are still running at the time of writing.
Tong, Juxiu; Hu, Bill X; Yang, Jinzhong; Zhu, Yan
2016-06-01
The mixing layer theory is not suitable for predicting solute transfer from initially saturated soil to surface runoff water under controlled drainage conditions. By coupling the mixing layer theory model with the numerical model Hydrus-1D, a hybrid solute transfer model has been proposed to predict soil solute transfer from an initially saturated soil into surface water, under controlled drainage water conditions. The model can also consider the increasing ponding water conditions on soil surface before surface runoff. The data of solute concentration in surface runoff and drainage water from a sand experiment is used as the reference experiment. The parameters for the water flow and solute transfer model and mixing layer depth under controlled drainage water condition are identified. Based on these identified parameters, the model is applied to another initially saturated sand experiment with constant and time-increasing mixing layer depth after surface runoff, under the controlled drainage water condition with lower drainage height at the bottom. The simulation results agree well with the observed data. Study results suggest that the hybrid model can accurately simulate the solute transfer from initially saturated soil into surface runoff under controlled drainage water condition. And it has been found that the prediction with increasing mixing layer depth is better than that with the constant one in the experiment with lower drainage condition. Since lower drainage condition and deeper ponded water depth result in later runoff start time, more solute sources in the mixing layer are needed for the surface water, and larger change rate results in the increasing mixing layer depth.
Hybrid fully nonlinear BEM-LBM numerical wave tank with applications in naval hydrodynamics
Mivehchi, Amin; Grilli, Stephan T.; Dahl, Jason M.; O'Reilly, Chris M.; Harris, Jeffrey C.; Kuznetsov, Konstantin; Janssen, Christian F.
2017-11-01
simulation of the complex dynamics response of ships in waves is typically modeled by nonlinear potential flow theory, usually solved with a higher order BEM. In some cases, the viscous/turbulent effects around a structure and in its wake need to be accurately modeled to capture the salient physics of the problem. Here, we present a fully 3D model based on a hybrid perturbation method. In this method, the velocity and pressure are decomposed as the sum of an inviscid flow and viscous perturbation. The inviscid part is solved over the whole domain using a BEM based on cubic spline element. These inviscid results are then used to force a near-field perturbation solution on a smaller domain size, which is solved with a NS model based on LBM-LES, and implemented on GPUs. The BEM solution for large grids is greatly accelerated by using a parallelized FMM, which is efficiently implemented on large and small clusters, yielding an almost linear scaling with the number of unknowns. A new representation of corners and edges is implemented, which improves the global accuracy of the BEM solver, particularly for moving boundaries. We present model results and the recent improvements of the BEM, alongside results of the hybrid model, for applications to problems. Office of Naval Research Grants N000141310687 and N000141612970.
Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach
Geng, Xiaolong; Boufadel, Michel C.; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L.; Miller, Richard S.
2014-09-01
A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies.
Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach.
Geng, Xiaolong; Boufadel, Michel C; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L; Miller, Richard S
2014-09-01
A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies. Copyright © 2014 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Elmira Ashpazzadeh
2018-04-01
Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
A numerical method for finding sign-changing solutions of superlinear Dirichlet problems
Energy Technology Data Exchange (ETDEWEB)
Neuberger, J.M.
1996-12-31
In a recent result it was shown via a variational argument that a class of superlinear elliptic boundary value problems has at least three nontrivial solutions, a pair of one sign and one which sign changes exactly once. These three and all other nontrivial solutions are saddle points of an action functional, and are characterized as local minima of that functional restricted to a codimension one submanifold of the Hilbert space H-0-1-2, or an appropriate higher codimension subset of that manifold. In this paper, we present a numerical Sobolev steepest descent algorithm for finding these three solutions.
COMPARING NUMERICAL METHODS FOR THE SOLUTION OF THE DAMPED FORCED OSCILLATOR PROBLEM
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A. R. Vahidi
2009-07-01
Full Text Available In this paper, we present a comparative study between the Adomian decomposition method and two classical well-known Runge-Kutta and central difference methods for the solution of damped forced oscillator problem. We show that the Adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.
Symmetry and Numerical Solutions for Systems of Non-linear Reaction Diffusion Equations
KUMAR,SANJEEV; Singh, Ravendra
2007-01-01
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion equation with respect to one-dimensional Algebra is carried out in this work. Some classes of analytical and numerical solutions are obtained and expressed using suitable graphs.
On the numerical solution of diffusion-reaction equations with singular source terms
Ashyraliyev, M.; Blom, J.G.; Verwer, J.G.
2008-01-01
A numerical study is presented of reaction-diffusion problems having singular reaction source terms, singular in the sense that within the spatial domain the source is defined by a Dirac delta function expression on a lower dimensional surface.A consequence is that solutions will be continuous, but
On the numerical solution of diffusion-reaction equations with singular source terms
M. Ashyraliyev (Maksat); J.G. Blom (Joke); J.G. Verwer (Jan)
2008-01-01
htmlabstractA numerical study is presented of reaction–diffusion problems having singular reaction source terms, singular in the sense that within the spatial domain the source is defined by a Dirac delta function expression on a lower dimensional surface. A consequence is that solutions will be
Numerical solutions of stochastic Lotka-Volterra equations via operational matrices
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F. Hosseini Shekarabi
2016-03-01
Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.
A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations
Diethelm, Kai; Ford, Neville J.; Freed, Alan D.; Gray, Hugh R. (Technical Monitor)
2002-01-01
We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.
Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...
Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different var...
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SURE KÖME
2014-12-01
Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.
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Zhanhua Yu
2011-01-01
Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.
Simple Hybrid Scaling-Free CORDIC Solution for FPGAs
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Leonid Moroz
2014-01-01
Full Text Available COordinate Rotation DIgital Computer (CORDIC is an effective method that is used in digital signal processing applications for computing various trigonometric, hyperbolic, linear, and transcendental functions. This paper presents the theoretical basis and practical implementation of circular (sine-cosine CORDIC-based generator. Synthesis results of this generator based on Altera Stratix III FPGA (EP3SL340F1517C2 using Quartus II version 9.0 show that the proposed hybrid FPGA architecture significantly reduces latency (42% reduction with a small area overhead, compared to the conventional version. The proposed algorithm has been simulated for sine and cosine function evaluation, and it has been verified that the accuracy is comparable with conventional algorithm.
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Andrea Lani
2006-01-01
Full Text Available Object-oriented platforms developed for the numerical solution of PDEs must combine flexibility and reusability, in order to ease the integration of new functionalities and algorithms. While designing similar frameworks, a built-in support for high performance should be provided and enforced transparently, especially in parallel simulations. The paper presents solutions developed to effectively tackle these and other more specific problems (data handling and storage, implementation of physical models and numerical methods that have arisen in the development of COOLFluiD, an environment for PDE solvers. Particular attention is devoted to describe a data storage facility, highly suitable for both serial and parallel computing, and to discuss the application of two design patterns, Perspective and Method-Command-Strategy, that support extensibility and run-time flexibility in the implementation of physical models and generic numerical algorithms respectively.
Edwin Tazelaar; P.P.J. van den Bosch; M. Grimminck; Bram Veenhuizen; Stijn Hoppenbrouwers
2011-01-01
The objective of an energy management strategy for fuel cell hybrid propulsion systems is to minimize the fuel needed to provide the required power demand. This minimization is defined as an optimization problem. Methods such as dynamic programming numerically solve this optimization problem.
Analytical solution of the energy management for fuel cell hybrid propulsion systems
Bram Veenhuizen; P.P.J. van den Bosch; E. Tazelaar
2012-01-01
The objective of an energy management strategy for fuel cell hybrid propulsion systems is to minimize the fuel needed to provide the required power demand. This minimization is defined as an optimization problem. Methods such as dynamic programming numerically solve this optimization problem.
Schuster, Jonathan
Infrared (IR) detectors are well established as a vital sensor technology for military, defense and commercial applications. Due to the expense and effort required to fabricate pixel arrays, it is imperative to develop numerical simulation models to perform predictive device simulations which assess device characteristics and design considerations. Towards this end, we have developed a robust three-dimensional (3D) numerical simulation model for IR detector pixel arrays. We used the finite-difference time-domain technique to compute the optical characteristics including the reflectance and the carrier generation rate in the device. Subsequently, we employ the finite element method to solve the drift-diffusion equations to compute the electrical characteristics including the I(V) characteristics, quantum efficiency, crosstalk and modulation transfer function. We use our 3D numerical model to study a new class of detector based on the nBn-architecture. This detector is a unipolar unity-gain barrier device consisting of a narrow-gap absorber layer, a wide-gap barrier layer, and a narrow-gap collector layer. We use our model to study the underlying physics of these devices and to explain the anomalously long lateral collection lengths for photocarriers measured experimentally. Next, we investigate the crosstalk in HgCdTe photovoltaic pixel arrays employing a photon-trapping (PT) structure realized with a periodic array of pillars intended to provide broadband operation. The PT region drastically reduces the crosstalk; making the use of the PT structures not only useful to obtain broadband operation, but also desirable for reducing crosstalk, especially in small pitch detector arrays. Then, the power and flexibility of the nBn architecture is coupled with a PT structure to engineer spectrally filtering detectors. Last, we developed a technique to reduce the cost of large-format, high performance HgCdTe detectors by nondestructively screen-testing detector arrays prior
Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model
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Nikola V. Georgiev
2003-01-01
Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.
NUMERICAL SOLUTION OF THE GODUNOV - SULTANGAZIN SYSTEM OF EQUATIONS. PERIODIC CASE
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Vasil’eva Ol’ga Aleksandrovna
2016-04-01
Full Text Available The Cauchy problem of the Godunov - Sultangazin system of equations with periodic initial conditions is considered in the article. The Godunov - Sultangazin system of equations is a model problem of the kinetic theory of gases. It is a discrete kinetic model of one-dimensional gas consisting of identical monatomic molecules. The molecules can have one of three speeds. So, there are three groups of molecules. The molecules of the first two groups have the speeds equal in values and opposite in directions. The molecules of the third group have zero speed. The considered mathematical model has a number of properties of Boltzmann equation. This system of the equations is a quasi-linear system of partial differential equations. There is no analytic solution for this problem in the general case. So, numerical investigation of the Cauchy problem of the Godunov - Sultangazin system is very important. The finite-difference method of the first order is used for numerical investigation of the Cauchy problem of the Godunov - Sultangazin system of equations. The paper presents and discusses the results of numerical investigation of the Cauchy problem for the studied system solution with periodic initial condition. The dependence of the time of stabilization of the Cauchy problem solution of Godunov - Sultangazin system of equations from the decreasing parameter of system are obtained. The paper presents the dependence of time of energy exchange from the decreasing parameter. The solution stabilization to the equilibrium state is obtained. The stabilization time of Godunov - Sultangazin system solution is compared to the stabilization time of Carleman system solution in periodic case. The results of numerical investigation are in good agreement with the theoretical results obtained previously.
Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium
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M. A. Castro
2013-01-01
conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.
Alfonso, Lester; Zamora, Jose; Cruz, Pedro
2015-04-01
The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.
Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
Madzvamuse, Anotida; Maini, Philip K.
2007-07-01
Reaction-diffusion systems have been widely studied in developmental biology, chemistry and more recently in financial mathematics. Most of these systems comprise nonlinear reaction terms which makes it difficult to find closed form solutions. It therefore becomes convenient to look for numerical solutions: finite difference, finite element, finite volume and spectral methods are typical examples of the numerical methods used. Most of these methods are locally based schemes. We examine the implications of mesh structure on numerically computed solutions of a well-studied reaction-diffusion model system on two-dimensional fixed and growing domains. The incorporation of domain growth creates an additional parameter - the grid-point velocity - and this greatly influences the selection of certain symmetric solutions for the ADI finite difference scheme when a uniform square mesh structure is used. Domain growth coupled with grid-point velocity on a uniform square mesh stabilises certain patterns which are however very sensitive to any kind of perturbation in mesh structure. We compare our results to those obtained by use of finite elements on unstructured triangular elements.
Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo
2016-05-01
We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.
A New Method to Solve Numeric Solution of Nonlinear Dynamic System
Directory of Open Access Journals (Sweden)
Min Hu
2016-01-01
Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.
Numerical solution of continuous-time DSGE models under Poisson uncertainty
DEFF Research Database (Denmark)
Posch, Olaf; Trimborn, Timo
then use the Waveform Relaxation algorithm to provide a guess of the policy function and solve the resulting system of ordinary differential equations by standard methods and fix-point iteration. Analytical solutions are provided as a benchmark from which our numerical method can be used to explore broader......We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic differential equations into a system of functional differential equations of the retarded type. We...
A numerical solution of a singular boundary value problem arising in boundary layer theory.
Hu, Jiancheng
2016-01-01
In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.
Directory of Open Access Journals (Sweden)
Thoudam Roshan
2016-10-01
Full Text Available Numerical solutions of the coupled Klein-Gordon-Schrödinger equations is obtained by using differential quadrature methods based on polynomials and quintic B-spline functions for space discretization and Runge-Kutta fourth order for time discretization. Stability of the schemes are studied using matrix stability analysis. The accuracy and efficiency of the methods are shown by conducting some numerical experiments on test problems. The motion of single soliton and interaction of two solitons are simulated by the proposed methods.
Solution processable organic/inorganic hybrid ultraviolet photovoltaic detector
Directory of Open Access Journals (Sweden)
Xiaopeng Guo
2016-05-01
Full Text Available Ultraviolet (UV photodetector is a kind of important optoelectronic device which can be widely used in scientific and engineering fields including astronomical research, environmental monitoring, forest-fire prevention, medical analysis, and missile approach warning etc. The development of UV detector is hindered by the acquirement of stable p-type materials, which makes it difficult to realize large array, low-power consumption UV focal plane array (FPA detector. Here, we provide a novel structure (Al/Poly(9,9-di-n-octylfuorenyl-2,7-diyl(PFO/ZnO/ITO to demonstrate the UV photovoltaic (PV response. A rather smooth surface (RMS roughness: 0.28 nm may be reached by solution process, which sheds light on the development of large-array, light-weight and low-cost UV FPA detectors.
Three-dimensional numerical and experimental studies on transient ignition of hybrid rocket motor
Tian, Hui; Yu, Ruipeng; Zhu, Hao; Wu, Junfeng; Cai, Guobiao
2017-11-01
This paper presents transient simulations and experimental studies of the ignition process of the hybrid rocket motors (HRMs) using 90% hydrogen peroxide (HP) as the oxidizer and polymethyl methacrylate (PMMA) and Polyethylene (PE) as fuels. A fluid-solid coupling numerically method is established based on the conserved form of the three-dimensional unsteady Navier-Stokes (N-S) equations, considering gas fluid with chemical reactions and heat transfer between the fluid and solid region. Experiments are subsequently conducted using high-speed camera to record the ignition process. The flame propagation, chamber pressurizing process and average fuel regression rate of the numerical simulation results show good agreement with the experimental ones, which demonstrates the validity of the simulations in this study. The results also indicate that the flame propagation time is mainly affected by fluid dynamics and it increases with an increasing grain port area. The chamber pressurizing process begins when the flame propagation completes in the grain port. Furthermore, the chamber pressurizing time is about 4 times longer than the time of flame propagation.
Numerical Study on Nonlinear Semiactive Control of Steel-Concrete Hybrid Structures Using MR Dampers
Directory of Open Access Journals (Sweden)
Long-He Xu
2013-01-01
Full Text Available Controlling the damage process, avoiding the global collapse, and increasing the seismic safety of the super high-rise building structures are of great significance to the casualties’ reduction and seismic losses mitigation. In this paper, a semiactive control platform based on magnetorheological (MR dampers comprising the Bouc-Wen model, the semi-active control law, and the shear wall damage criteria and steel damage material model is developed in LS-DYNA program, based on the data transferring between the main program and the control platform; it can realize the purpose of integrated modeling, analysis, and design of the nonlinear semi-active control system. The nonlinear seismic control effectiveness is verified by the numerical example of a 15-story steel-concrete hybrid structure; the results indicate that the control platform and the numerical method are stable and fast, the relative displacement, shear force, and damage of the steel-concrete structure are largely reduced using the optimal designed MR dampers, and the deformations and shear forces of the concrete tube and frame are better consorted by the control devices.
Numerical time-dependent solutions of the Schrödinger equation with piecewise continuous potentials
van Dijk, Wytse
2016-06-01
We consider accurate numerical solutions of the one-dimensional time-dependent Schrödinger equation when the potential is piecewise continuous. Spatial step sizes are defined for each of the regions between the discontinuities and a matching condition at the boundaries of the regions is employed. The Numerov method for spatial integration is particularly appropriate to this approach. By employing Padé approximants for the time-evolution operator, we obtain solutions with significantly improved precision without increased CPU time. This approach is also appropriate for adaptive changes in spatial step size even when there is no discontinuity of the potential.
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C. A. Raposo
2013-08-01
Full Text Available In this work we study the asymptotic behavior as t → ∞ of the solution for the Timoshenko system with delay term in the feedback. We use the semigroup theory for to prove the well-posedness of the system and for to establish the exponential stability. As far we know, there exist few results for problems with delay, where the asymptotic behavior is based on the Gearhart- Herbst-Pruss-Huang theorem to dissipative system. See [4], [5], [6]. Finally, we present numerical results of the solution of the system.
Directory of Open Access Journals (Sweden)
Pradeep Jangir
2017-04-01
Full Text Available Recent trend of research is to hybridize two and more algorithms to obtain superior solution in the field of optimization problems. In this context, a new technique hybrid Particle Swarm Optimization (PSO-Multi verse Optimizer (MVO is exercised on some unconstraint benchmark test functions and the most common problem of the modern power system named Optimal Reactive Power Dispatch (ORPD is optimized using the novel hybrid meta-heuristic optimization algorithm Particle Swarm Optimization-Multi Verse Optimizer (HPSO-MVO method. Hybrid PSO-MVO is combination of PSO used for exploitation phase and MVO for exploration phase in uncertain environment. Position and Speed of particle is modernised according to location of universes in each iteration. The hybrid PSO-MVO method has a fast convergence rate due to use of roulette wheel selection method. For the ORPD solution, standard IEEE-30 bus test system is used. The hybrid PSO-MVO method is implemented to solve the proposed problem. The problems considered in the ORPD are fuel cost reduction, Voltage profile improvement, Voltage stability enhancement, Active power loss minimization and Reactive power loss minimization. The results obtained with hybrid PSO-MVO method is compared with other techniques such as Particle Swarm Optimization (PSO and Multi Verse Optimizer (MVO. Analysis of competitive results obtained from HPSO-MVO validates its effectiveness compare to standard PSO and MVO algorithm.
An efficient numerical technique for the solution of nonlinear singular boundary value problems
Singh, Randhir; Kumar, Jitendra
2014-04-01
In this work, a new technique based on Green's function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Green's function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several numerical examples. The numerical results reveal that the proposed method is very efficient and accurate.
Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior
Directory of Open Access Journals (Sweden)
F. Ghomanjani
2014-01-01
Full Text Available We present a numerical method to solve boundary value problems (BVPs for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, into k subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree n and determined Bezier curves on any subinterval by n+1 control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems.
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H. Khalil
2015-06-01
Full Text Available We study shifted Legendre polynomials and develop some operational matrices of integrations. We use these operational matrices and develop new sophisticated technique for numerical solutions to the following coupled system of fredholm integro differential equations DU(x = f(x + 11 Z 1 0 K11(x, tU(tdt + 12 Z 1 0 K12(x, tV (tdt, DV (x = g(x + 21 Z 1 0 K21(x, tU(tdt + 22 Z 1 0 K22(x, tV (tdt, U(0 = C1, V (0 = C2, where D is fractional derivative of order with respect to x, 0 < 6 1, 11, 12, 21, 22 are real constants, f, g 2 C([0, 1] and K11, K12, K21, K22 2 C([0, 1]×[0, 1]. We develop simple procedure to reduce the coupled system of equations to a system of algebraic equations without discretizing the system. We provide examples and numerical simulations to show the applicability and simplicity of our results and to demonstrate that the results obtained using the new technique matches well with the exact solutions of the problem. We also provide error analysis.
Optimality conditions for the numerical solution of optimization problems with PDE constraints :
Energy Technology Data Exchange (ETDEWEB)
Aguilo Valentin, Miguel Alejandro; Ridzal, Denis
2014-03-01
A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.
A Comparative Evaluation of Numerical and Analytical Solutions to the Biadhesive Single-Lap Joint
Halil Özer; Özkan Öz
2014-01-01
This paper attempts to address the detailed verification of Zhao’s analytical solution including the moment effect with the two- and three-dimensional finite element results. Zhao compared the analytical results with only the 2D FEA results and used the constant bond-length ratio for the biadhesive bondline. In this study, overlap surfaces of the adherends and the adhesives were modelled using surface-to-surface contact elements. Both analytical and numerical analyses were performed using fou...
Shiralashetti, S. C.; Deshi, A. B.
Wavelet analysis is a recently developed mathematical tool for many problems. One of its main attractive features is the ability to accurately represent general functions with small number of adaptively chosen wavelet coefficients. In this paper, the Legendre wavelet collocation method (LWCM) for the numerical solution of differential equations is presented. The proposed method gives better results than the existing ones. Some of the illustrative examples are included to observe the performance of the proposed scheme.
The Navier-Stokes-Fourier system: From weak solutions to numerical analysis
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2015-01-01
Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml
Numerical solutions of the Kawahara equation by the septic B-spline collocation method
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Battal Gazi Karakoc
2014-08-01
Full Text Available In this article, a numerical solution of the Kawahara equation is presented by septic B-spline collocation method. Applying the Von-Neumann stability analysis, the present method is shown to be unconditionally stable. The accuracy of the proposed method is checked by two test problems. L2 and L1 error norms and conserved quantities are given at selected times. The obtained results are found in good agreement with the some recent results.
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Andreas Ruffing
2001-01-01
Full Text Available We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics.
The numerical solution of differential-algebraic systems by Runge-Kutta methods
Hairer, Ernst; Lubich, Christian
1989-01-01
The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.
A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation
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Hakon A. Hoel
2007-07-01
Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.
Numerical solution of linear Klein-Gordon equation using FDAM scheme
Kasron, Noraini; Suharto, Erni Suryani; Deraman, Ros Fadilah; Othman, Khairil Iskandar; Nasir, Mohd Agos Salim
2017-05-01
Many scientific areas appear in a hyperbolic partial differential equation like the Klien-Gordon equation. The analytical solutions of the Klein-Gordon equation have been approximated by the suggested numerical approaches. However, the arithmetic mean (AM) method has not been studied on the Klein-Gordon equation. In this study, a new proposed scheme has utilized central finite difference formula in time and space (CTCS) incorporated with AM formula averaging of functional values for approximating the solutions of the Klein-Gordon equation. Three-point AM is considered to a linear inhomogeneous Klein-Gordon equation. The theoretical aspects of the numerical scheme for the Klein-Gordon equation are also considered. The stability analysis is analyzed by using von Neumann stability analysis and Miller Norm Lemma. Graphical results verify the necessary conditions of Miller Norm Lemma. Good results obtained relate to the theoretical aspects of the numerical scheme. The numerical experiments are examined to verify the theoretical analysis. Comparative study shows the new CTCS scheme incorporated with three-point AM method produced better accuracy and shown its reliable and efficient over the standard CTCS scheme.
Ortleb, Sigrun; Seidel, Christian
2017-07-01
In this second symposium at the limits of experimental and numerical methods, recent research is presented on practically relevant problems. Presentations discuss experimental investigation as well as numerical methods with a strong focus on application. In addition, problems are identified which require a hybrid experimental-numerical approach. Topics include fast explicit diffusion applied to a geothermal energy storage tank, noise in experimental measurements of electrical quantities, thermal fluid structure interaction, tensegrity structures, experimental and numerical methods for Chladni figures, optimized construction of hydroelectric power stations, experimental and numerical limits in the investigation of rain-wind induced vibrations as well as the application of exponential integrators in a domain-based IMEX setting.
H. van Dekken (Herman); F.T.B. Bosman (Fré); R. Teijgeman (R.); K.J. Vissers (Kees); T.A. Tersteeg (T.); H.M.J. Kerstens (H. M J); M. Vooijs (Marc); A.A. Verhofstad (Albert)
1993-01-01
textabstractWe have applied non-isotopic in situ hybridization (ISH) to interphase cell nuclei of 23 phaeochromocytomas (18 primary and 5 metastatic tumours) within routine paraffin-embedded tissue sections. Each tumour was screened for numerical aberrations with a defined alphoid repetitive DNA
An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere
Swidinsky, Andrei; Liu, Lifei
2017-11-01
We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.
Energy Technology Data Exchange (ETDEWEB)
Ojeda Gonzalez, A.; Domingues, M.O.; Mendes, O., E-mail: ojeda.gonzalez.a@gmail.com [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil); Kaibara, M.K. [Universidade Federal Fluminense (GMA/IME/UFF), Niteroi, RJ (Brazil); Prestes, A. [Universidade do Vale do Paraiba (IP and D/UNIVAP), Sao Jose dos Campos, SP (Brazil). Lab. de Fisica e Astronomia
2015-10-15
The Grad-Shafranov equation is a Poisson's equation, i.e., a partial differential equation of elliptic type. The problem is depending on the initial condition and can be treated as a Cauchy problem. Although it is ill-posed or ill-conditioned, it can be integrated numerically. In the integration of the GS equation, singularities with large values of the potential arise after a certain number of integration steps away from the original data line, and a filter should be used. The Grad-Shafranov reconstruction (GSR) technique was developed from 1996 to 2000 for recovering two-dimensional structures in the magnetopause in an ideal MHD formulation. Other works have used the GSR techniques to study magnetic flux ropes in the solar wind and in the magnetotail from a single spacecraft dataset; posteriorly, it was extended to treat measurements from multiple satellites. From Vlasov equation, it is possible to arrive at the GS-equation in function of the normalized vector potential. A general solution is obtained using complex variable theory. A specific solution was chosen as benchmark case to solve numerically the GS equation.We propose some changes in the resolution scheme of the GS equation to improve the solution. The result of each method is compared with the solution proposed by Hau and Sonnerup (J. Geophys. Res. 104(A4), 6899-6917 (1999)). The main improvement found in the GS resolution was the need to filter Bx values at each y value. (author)
A hybrid numerical-experimental study of fluid transport by migrating zooplankton aggregations
Martinez, Monica; Dabiri, John; Nawroth, Janna; Gemmell, Brad; Collins, Samantha
2014-11-01
Zooplankton aggregations that undergo diel vertical migrations have been hypothesized to play an important role in local nutrient transport and global ocean dynamics. The degree of the contributions of these naturally occurring events ultimately relies on how efficiently fluid is transported and eventually mixed within the water column. By implementing solutions to the Stokes equations, numerical models have successfully captured the time-averaged far-field flow of self-propelled swimmers. However, discrepancies between numerical fluid transport estimates and field measurements of individual jellyfish suggest the need to include near-field effects to assess the impact of biomixing in oceanic processes. Here, we bypass the inherent difficulty of modeling the unsteady flow of active swimmers while including near-field effects by integrating experimental velocity data of zooplankton into our numerical model. Fluid transport is investigated by tracking a sheet of artificial fluid particles during vertical motion of zooplankton. Collective effects are addressed by studying different swimmer configurations within an aggregation from the gathered data for a single swimmer. Moreover, the dependence of animal swimming mode is estimated by using data for different species of zooplankton.
A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation
Liu, Yang
2010-03-01
We propose an efficient scheme to absorb reflections from the model boundaries in numerical solutions of wave equations. This scheme divides the computational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and the one-way wave equation, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the one-way wave equation to obtain a smooth variation from the inner area to the boundary via the transition zone. The results from our finite-difference numerical modeling tests of the 2D acoustic wave equation show that the absorption enforced by this scheme gradually increases with increasing width of the transition area. We obtain equally good performance using pseudospectral and finite-element modeling with the same scheme. Our numerical experiments demonstrate that use of 10 grid points for absorbing edge reflections attains nearly perfect absorption. © 2010 Society of Exploration Geophysicists.
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Vineet K. Srivastava
2014-03-01
Full Text Available In this paper, an implicit logarithmic finite difference method (I-LFDM is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.
Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report
Energy Technology Data Exchange (ETDEWEB)
Prinja, Anil K.
2000-12-31
The overall goal of this project was to develop advanced theoretical and numerical techniques to quantitatively describe the spreading of a collimated beam of charged particles in space, in angle, and in energy, as a result of small deflection, small energy transfer Coulomb collisions with the target nuclei and electrons. Such beams arise in several applications of great interest in nuclear engineering, and include electron and ion radiotherapy, ion beam modification of materials, accelerator transmutation of waste, and accelerator production of tritium, to name some important candidates. These applications present unique and difficult modeling challenges, but from the outset are amenable to the language of ''transport theory'', which is very familiar to nuclear engineers and considerably less-so to physicists and material scientists. Thus, our approach has been to adopt a fundamental description based on transport equations, but the forward peakedness associated with charged particle interactions precludes a direct application of solution methods developed for neutral particle transport. Unique problem formulations and solution techniques are necessary to describe the transport and interaction of charged particles. In particular, we have developed the Generalized Fokker-Planck (GFP) approach to describe the angular and radial spreading of a collimated beam and a renormalized transport model to describe the energy-loss straggling of an initially monoenergetic distribution. Both analytic and numerical solutions have been investigated and in particular novel finite element numerical methods have been developed. In the first phase of the project, asymptotic methods were used to develop closed form solutions to the GFP equation for different orders of expansion, and was described in a previous progress report. In this final report we present a detailed description of (i) a novel energy straggling model based on a Fokker-Planck approximation but
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H.M. Nasir
2016-05-01
Full Text Available Heavy metal contamination in the environment could cause harmful effects both to human health and aquatic life. Numerous remediation methods had been developed to encounter with the contamination problem prior to degrade, decrease and to purify the contaminated water at minimal concentration as low as possible. Therefore, in current study, commercialized chicken eggshells and hybrid Akar Putra chicken eggshells were conducted in batch experiment to testify the capabilities of bio-sorbent materials in iron (II ion removal from aqueous solution at optimized level of dosage and equilibrium contact time. The optimum condition for iron (II removal for commercialized chicken eggshells and hybrid Akar Putra chicken eggshells bio-sorbents reached at 0.30 g with optimum contact time of 50 minutes and 91.83% and 91.07% of removal percentage with 0.60 g at 40 minutes. The final concentration from both bio-sorbents is achieved below than drinking water guideline (0.30 mg/L, 0.1635 mg/L and 0.1785 mg/L, respectively. The isotherm adsorption results showed it fitted better in Langmuir Isotherm Model than in Freundlich Isotherm Model, however with weak bonding, which could not held onto the heavy metal ions in long time period. In brief, commercialized chicken eggshells and hybrid Akar Putra chicken eggshells have considerable potential in removing heavy metal in aqueous solution. The selection of the bio-sorbent materials is more favorable as it reduces dependency towards chemical usage in water treatment which could have complied with drinking water guideline that can be obtained easily, abundance in amount, cheap and biodegradable.
Synthesis and photocatalytic activity of Pt-ZnO hybrid nanocomposite by solution plasma technology.
Hu, Xiulan; Xu, QiuCheng; Ge, Chao; Su, Nan; Zhang, Jianbo; Huang, Huihong; Zhu, Shoufeng; Xu, Yanqiu; Cheng, Jiexu
2017-01-27
In this paper, Pt-ZnO hybrid nanocomposites were prepared by solution plasma technology. X-ray diffraction (XRD) and energy dispersive x-ray analysis (EDX) were used to verify their chemical composition. The size and morphology of the Pt-ZnO hybrid nanocomposites were characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). These results indicate that about 2-3 nm Pt nanoparticles (NPs) were synthesized and dispersed on the pyramid-like ZnO (20-60 nm) surface. Photodegradation of Rhodamine B (RhB) demonstrates that the Pt (5 wt%)-ZnO hybrid nanocomposite has better photocatalytic activity than commercial P25 because Pt NPs restrain the photogenerated electron/hole recombination and increase the catalyst activity.
On the numerical solution of the one-dimensional convection-diffusion equation
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Dehghan Mehdi
2005-01-01
Full Text Available The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes several finite difference schemes for solving the one-dimensional convection-diffusion equation with constant coefficients. In this research the use of modified equivalent partial differential equation (MEPDE as a means of estimating the order of accuracy of a given finite difference technique is emphasized. This approach can unify the deduction of arbitrary techniques for the numerical solution of convection-diffusion equation. It is also used to develop new methods of high accuracy. This approach allows simple comparison of the errors associated with the partial differential equation. Various difference approximations are derived for the one-dimensional constant coefficient convection-diffusion equation. The results of a numerical experiment are provided, to verify the efficiency of the designed new algorithms. The paper ends with a concluding remark.
2013-01-01
The main goal of this book is to provide a state of the art of hybrid metaheuristics. The book provides a complete background that enables readers to design and implement hybrid metaheuristics to solve complex optimization problems (continuous/discrete, mono-objective/multi-objective, optimization under uncertainty) in a diverse range of application domains. Readers learn to solve large scale problems quickly and efficiently combining metaheuristics with complementary metaheuristics, mathematical programming, constraint programming and machine learning. Numerous real-world examples of problems and solutions demonstrate how hybrid metaheuristics are applied in such fields as networks, logistics and transportation, bio-medical, engineering design, scheduling.
Moszczyński, P.; Walczak, A.; Marciniak, P.
2016-12-01
In cyclic articles previously published we described and analysed self-organized light fibres inside a liquid crystalline (LC) cell contained photosensitive polymer (PP) layer. Such asymmetric LC cell we call a hybrid LC cell. Light fibre arises along a laser beam path directed in plane of an LC cell. It means that a laser beam is parallel to photosensitive layer. We observed the asymmetric LC cell response on an external driving field polarization. Observation has been done for an AC field first. It is the reason we decided to carry out a detailed research for a DC driving field to obtain an LC cell response step by step. The properly prepared LC cell has been built with an isolating layer and garbage ions deletion. We proved by means of a physical model, as well as a numerical simulation that LC asymmetric response strongly depends on junction barriers between PP and LC layers. New parametric model for a junction barrier on PP/LC boundary has been proposed. Such model is very useful because of lack of proper conductivity and charge carriers of band structure data on LC material.
Fast Hybrid MPPT Technique for Photovoltaic Applications: Numerical and Experimental Validation
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Gianluca Aurilio
2014-01-01
Full Text Available In PV applications, under mismatching conditions, it is necessary to adopt a maximum power point tracking (MPPT technique which is able to regulate not only the voltages of the PV modules of the array but also the DC input voltage of the inverter. Such a technique can be considered a hybrid MPPT (HMPPT technique since it is neither only distributed on the PV modules of the PV array or only centralized at the input of the inverter. In this paper a new HMPPT technique is presented and discussed. Its main advantages are the high MPPT efficiency and the high speed of tracking which are obtained by means of a fast estimate of the optimal values of PV modules voltages and of the input inverter voltage. The new HMPPT technique is compared with simple HMPPT techniques based on the scan of the power versus voltage inverter input characteristic. The theoretical analysis and the results of numerical simulations are widely discussed. Moreover, a laboratory test system, equipped with PV emulators, has been realized and used in order to experimentally validate the proposed technique.
Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems
Frohne, Jörg
2015-08-06
© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.
The numerical solution of thawing process in phase change slab using variable space grid technique
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Serttikul, C.
2007-09-01
Full Text Available This paper focuses on the numerical analysis of melting process in phase change material which considers the moving boundary as the main parameter. In this study, pure ice slab and saturated porous packed bed are considered as the phase change material. The formulation of partial differential equations is performed consisting heat conduction equations in each phase and moving boundary equation (Stefan equation. The variable space grid method is then applied to these equations. The transient heat conduction equations and the Stefan condition are solved by using the finite difference method. A one-dimensional melting model is then validated against the available analytical solution. The effect of constant temperature heat source on melting rate and location of melting front at various times is studied in detail.It is found that the nonlinearity of melting rate occurs for a short time. The successful comparison with numerical solution and analytical solution should give confidence in the proposed mathematical treatment, and encourage the acceptance of this method as useful tool for exploring practical problems such as forming materials process, ice melting process, food preservation process and tissue preservation process.
He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J.; Zhan, Hongbin
2017-11-01
Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions.
He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J; Zhan, Hongbin
2017-11-01
Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions. Copyright © 2017 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
Markos, Christos
2016-01-01
The possibility to combine silica photonic crystal fiber (PCF) as low-loss platform with advanced functional materials, offers an enormous range of choices for the development of fiber-based tunable devices. Here, we report a tunable hybrid silica PCF with integrated As2S3 glass nanolayers inside...... the air-capillaries of the fiber based on a solution-processed glass approach. The deposited high-index layers revealed antiresonant transmission windows from similar to 500 nm up to similar to 1300 nm. We experimentally demonstrate for the first time the possibility to thermally-tune the revealed...... antiresonances by taking advantage the high thermo-optic coefficient of the solution-processed nanolayers. Two different hybrid fiber structures, with core diameter 10 and 5 mu m, were developed and characterized using a supercontinuum source. The maximum sensitivity was measured to be as high as 3.6 nm...
Directory of Open Access Journals (Sweden)
Chau Dinh Van
2015-01-01
Full Text Available The fabrication and the property investigation of the hybrid nanocomposite material made of poly[2-methoxy-5-(2′-ethyl-hexyloxy-1,4-phenylene vinylene] (MEH-PPV polymer and Y3Al5O12:Ce (YAG:Ce with the relative weight ratio of 1 : 1 in order to apply for optoelectronic devices are reported. Thermal analysis showed the hybrid material’s deterioration or decomposition when the temperature exceeded 200°C under inert gas atmosphere. Rheological measurement concluded that the material solution can be used for spinning or soft moulding lithography making large- or flexible substrate surface. Optical properties of the hybrid material are investigated. The effect of thermal treatment on the optical properties showed that, at 180°C under inert gas environment, the optical properties were enhanced. An MEH-PPV/YAG:Ce hybrid nanocomposite converted LED lamp was fabricated showing that the hybrid material is suitable as conversion material for white LED fabrication.
Organic-Inorganic Hybrid Solution-Processed H₂-Evolving Photocathodes.
Lai, Lai-Hung; Gomulya, Widianta; Berghuis, Matthijs; Protesescu, Loredana; Detz, Remko J; Reek, Joost N H; Kovalenko, Maksym V; Loi, Maria A
2015-09-02
Here we report for the first time an H2-evolving photocathode fabricated by a solution-processed organic-inorganic hybrid composed of CdSe and P3HT. The CdSe:P3HT (10:1 (w/w)) hybrid bulk heterojunction treated with 1,2-ethanedithiol (EDT) showed efficient water reduction and hydrogen generation. A photocurrent of -1.24 mA/cm(2) at 0 V versus reversible hydrogen electrode (V(RHE)), EQE of 15%, and an unprecedented Voc of 0.85 V(RHE) under illumination of AM1.5G (100 mW/cm(2)) in mild electrolyte were observed. Time-resolved photoluminescence (TRPL), internal quantum efficiency (IQE), and transient photocurrent measurements were carried out to clarify the carrier dynamics of the hybrids. The exciton lifetime of CdSe was reduced by one order of magnitude in the hybrid blend, which is a sign of the fast charge separation upon illumination. By comparing the current magnitude of the solid-state devices and water-splitting devices made with identical active layers, we found that the interfaces of the water-splitting devices limit the device performance. The electron/hole transport properties investigated by comparing IQE spectra upon front- and back-side illumination evidenced balanced electron/hole transport. The Faradaic efficiency is 80-100% for the hybrid photocathodes with Pt catalysts and ∼70% for the one without Pt catalysts.
A Comparative Evaluation of Numerical and Analytical Solutions to the Biadhesive Single-Lap Joint
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Halil Özer
2014-01-01
Full Text Available This paper attempts to address the detailed verification of Zhao’s analytical solution including the moment effect with the two- and three-dimensional finite element results. Zhao compared the analytical results with only the 2D FEA results and used the constant bond-length ratio for the biadhesive bondline. In this study, overlap surfaces of the adherends and the adhesives were modelled using surface-to-surface contact elements. Both analytical and numerical analyses were performed using four different biadhesive bondline configurations. The 3D FEA results reveal the existence of complex stress state at the overlap ends. However, the general results show that analytical and numerical results were in a good agreement.
Cost-effective hybrid RF/FSO backhaul solution for next generation wireless systems
Dahrouj, Hayssam
2015-10-28
The rapid pace of demand for mobile data services and the limited supply of capacity in the current wireless access networks infrastructure are leading network operators to increase the density of base station deployments to improve network performance. This densification, made possible by small-cell deployment, also brings a novel set of challenges, specifically related to the cost of ownership, in which backhaul is of primary concern. This article proposes a cost-effective hybrid RF/free-space optical (FSO) solution to combine the advantages of RF backhauls (low cost, NLOS applications) and FSO backhauls (high-rate, low latency). To first illustrate the cost advantages of the RF backhaul solution, the first part of this article presents a business case of NLOS wireless RF backhaul, which has a low cost of ownership as compared to other backhaul candidates. RF backhaul, however, is limited by latency problems. On the other side, an FSO solution, which offers better latency and higher data rate than RF backhauls, remains sensitive to weather and nature conditions (e.g., rain, fog). To combine RF and FSO advantages, the second part of this article proposes a lowcost hybrid RF/FSO solution, wherein base stations are connected to each other using either optical fiber or hybrid RF/FSO links. This part addresses the problem of minimizing the cost of backhaul planning under reliability, connectivity, and data rate constraints, and proposes choosing the appropriate cost-effective backhaul connection between BSs (i.e., either OF or hybrid RF/FSO) using graph theory techniques.
Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations
Energy Technology Data Exchange (ETDEWEB)
Després, Bruno, E-mail: despres@ann.jussieu.fr [Laboratory Jacques Louis Lions, University Pierre et Marie Curie, Paris VI, Boîte courrier 187, 75252 Paris Cedex 05 (France); Weder, Ricardo, E-mail: weder@unam.mx [Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, DF 01000 (Mexico)
2016-03-22
We study the long-time asymptotic of the solutions to Maxwell's equation in the case of an upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Després, L.M. Imbert-Gérard and R. Weder (2014) [15], where the singular solutions to Maxwell's equations in the frequency domain were constructed by means of a limiting absorption principle and a formula for the heating of the plasma in the limit of vanishing collision frequency was obtained. Currently there is considerable interest in these problems, in particular, because upper-hybrid resonances are a possible scenario for the heating of plasmas, and since they can be a model for the diagnostics involving wave scattering in plasmas. - Highlights: • The upper-hybrid resonance in the cold plasma model is considered. • The long-time asymptotic of the solutions to Maxwell's equations is studied. • A method based in a singular limiting absorption principle is proposed.
Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem
Ceccobello, C.; Farinelli, R.; Titarchuk, L.
2014-01-01
We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the
Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes
Chesler, Paul M.; Yaffe, Laurence G.
2014-07-01
A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.
WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method
Crevoisier, David; Voltz, Marc
2013-04-01
To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute
Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations
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Yongjin Li
2017-01-01
Full Text Available We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs. We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique.
Directory of Open Access Journals (Sweden)
R. C. Mittal
2014-01-01
Full Text Available We present a technique based on collocation of cubic B-spline basis functions to solve second order one-dimensional hyperbolic telegraph equation with Neumann boundary conditions. The use of cubic B-spline basis functions for spatial variable and its derivatives reduces the problem into system of first order ordinary differential equations. The resulting system subsequently has been solved by SSP-RK54 scheme. The accuracy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and in good agreement with the exact solution.
Human-computer interfaces applied to numerical solution of the Plateau problem
Elias Fabris, Antonio; Soares Bandeira, Ivana; Ramos Batista, Valério
2015-09-01
In this work we present a code in Matlab to solve the Problem of Plateau numerically, and the code will include human-computer interface. The Problem of Plateau has applications in areas of knowledge like, for instance, Computer Graphics. The solution method will be the same one of the Surface Evolver, but the difference will be a complete graphical interface with the user. This will enable us to implement other kinds of interface like ocular mouse, voice, touch, etc. To date, Evolver does not include any graphical interface, which restricts its use by the scientific community. Specially, its use is practically impossible for most of the Physically Challenged People.
Numerical Solution of Problem for Non-Stationary Heat Conduction in Multi-Layer Bodies
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R. I. Еsman
2007-01-01
Full Text Available A mathematical model for non-stationary heat conduction of multi-layer bodies has been developed. Dirac’s δ-function is used to take into account phase and chemical transformations in one of the wall layers. While formulating a problem non-linear heat conduction equations have been used with due account of dependence of thermal and physical characteristics on temperature. Solution of the problem is realized with the help of methods of a numerical experiment and computer modeling.
DeChant, Lawrence Justin
1998-01-01
In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have
Thompson, J. F.; Warsi, Z. U. A.; Mastin, C. W.
1982-01-01
A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.
Numerical solution of quadratic matrix equations for free vibration analysis of structures
Gupta, K. K.
1975-01-01
This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.
A Numerical Algorithm for the Solution of a Phase-Field Model of Polycrystalline Materials
Energy Technology Data Exchange (ETDEWEB)
Dorr, M R; Fattebert, J; Wickett, M E; Belak, J F; Turchi, P A
2008-12-04
We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward difference formula (BDF) temporal discretization combined with a Newton-Krylov algorithm to solve the nonlinear system at each time step. The BDF algorithm is combined with a coordinate projection method to maintain quaternion unit length, which is related to an important solution invariant. A key element of the Newton-Krylov algorithm is the selection of a preconditioner to accelerate the convergence of the Generalized Minimum Residual algorithm used to solve the Jacobian linear system in each Newton step. Results are presented for the application of the algorithm to 2D and 3D examples.
Mustafa, Meraj; Farooq, Muhammad A; Hayat, Tasawar; Alsaedi, Ahmed
2013-01-01
This investigation is concerned with the stagnation-point flow of nanofluid past an exponentially stretching sheet. The presence of Brownian motion and thermophoretic effects yields a coupled nonlinear boundary-value problem (BVP). Similarity transformations are invoked to reduce the partial differential equations into ordinary ones. Local similarity solutions are obtained by homotopy analysis method (HAM), which enables us to investigate the effects of parameters at a fixed location above the sheet. The numerical solutions are also derived using the built-in solver bvp4c of the software MATLAB. The results indicate that temperature and the thermal boundary layer thickness appreciably increase when the Brownian motion and thermophoresis effects are strengthened. Moreover the nanoparticles volume fraction is found to increase when the thermophoretic effect intensifies.
Numerical Methods for Solution of the Extended Linear Quadratic Control Problem
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog
2012-01-01
In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....
Numerical Simulation of the Freeze-Thaw Behavior of Mortar Containing Deicing Salt Solution.
Esmaeeli, Hadi S; Farnam, Yaghoob; Bentz, Dale P; Zavattieri, Pablo D; Weiss, Jason
2017-02-01
This paper presents a one-dimensional finite difference model that is developed to describe the freeze-thaw behavior of an air-entrained mortar containing deicing salt solution. A phenomenological model is used to predict the temperature and the heat flow for mortar specimens during cooling and heating. Phase transformations associated with the freezing/melting of water/ice or transition of the eutectic solution from liquid to solid are included in this phenomenological model. The lever rule is used to calculate the quantity of solution that undergoes the phase transformation, thereby simulating the energy released/absorbed during phase transformation. Undercooling and pore size effects are considered in the numerical model. To investigate the effect of pore size distribution, this distribution is considered using the Gibbs-Thomson equation in a saturated mortar specimen. For an air-entrained mortar, the impact of considering pore size (and curvature) on freezing was relatively insignificant; however the impact of pore size is much more significant during melting. The fluid inside pores smaller than 5 nm (i.e., gel pores) has a relatively small contribution in the macroscopic freeze-thaw behavior of mortar specimens within the temperature range used in this study (i.e., +24 °C to -35 °C), and can therefore be neglected for the macroscopic freeze-thaw simulations. A heat sink term is utilized to simulate the heat dissipation during phase transformations. Data from experiments performed using a low-temperature longitudinal guarded comparative calorimeter (LGCC) on mortar specimens fully saturated with various concentration NaCl solutions or partially saturated with water is compared to the numerical results and a promising agreement is generally obtained.
Directory of Open Access Journals (Sweden)
Hui Wang
2013-01-01
Full Text Available The boundary-type hybrid finite element formulation coupling the Kirchhoff transformation is proposed for the two-dimensional nonlinear heat conduction problems in solids with or without circular holes, and the thermal conductivity of material is assumed to be in terms of temperature change. The Kirchhoff transformation is firstly used to convert the nonlinear partial differential governing equation into a linear one by introducing the Kirchhoff variable, and then the new linear system is solved by the present hybrid finite element model, in which the proper fundamental solutions associated with some field points are used to approximate the element interior fields and the conventional shape functions are employed to approximate the element frame fields. The weak integral functional is developed to link these two fields and establish the stiffness equation with sparse and symmetric coefficient matrix. Finally, the algorithm is verified on several examples involving various expressions of thermal conductivity and existence of circular hole, and numerical results show good accuracy and stability.
Numerical simulation of a hybrid CSP/Biomass 5 MWel power plant
Soares, João; Oliveira, Armando
2017-06-01
The fundamental benefit of using renewable energy systems is undeniable since they rely on a source that will not run out. Nevertheless, they strongly depend on meteorological conditions (solar, wind, etc.), leading to uncertainty of instantaneous energy supply and consequently to grid connection issues. An interesting concept is renewable hybridisation. This consists in the strategic combination of different renewable sources in the power generation portfolio by taking advantage of each technology. Hybridisation of concentrating solar power with biomass denotes a powerful way of assuring system stability and reliability. The main advantage is dispatchability through the whole extent of the operating range. Regarding concentrating solar power heat transfer fluid, direct steam generation is one of the most interesting concepts. Nevertheless, it presents itself technical challenges that are mostly related to the two-phase fluid flow in horizontal pipes, as well as the design of an energy storage system. Also, the use of reheat within the turbine is usually indirectly addressed, hindering system efficiency. These challenges can be addressed through hybridisation with biomass. In this paper, a hybrid renewable electricity generation system is presented. The system relies on a combination of solar and biomass sources to drive a 5 MWel steam turbine. System performance is analysed through numerical simulation using Ebsilon professional software. The use of direct reheat in the turbine is addressed. Results show that hybridisation results in an enhancement of system dispatchability and generation stability. Furthermore, hybridisation enhanced the annual solar field and power block efficiencies, and thus the system annual efficiency (from 7.6% to 20%). The use of direct reheat eliminates steam wetness in the last turbine stage and also improves system efficiency.
Numerical solution of an elastic and viscoelastic gravitational models by the finite element method
Arjona Almodóvar, A.; Chacón Rebollo, T.; Gómez Marmol, M.
2014-12-01
Volcanic areas present a lower effective viscosity than usually in the Earth's crust. Both the elastic-gravitational and the viscoelastic-gravitational models allow the computation of gravity, deformation, and gravitational potential changes in order to investigate crustal deformations of Earth (see for instance Battaglia & Segall, 2004; Fernández et al. 1999, 2001; Rundle 1980 and 1983). These models can be represented by a coupled system of linear parabolic (for the elastic deformations), hyperbolic (for the viscoelastic deformations) and elliptic partial differential equations (for gravitational potential changes) (see for instance Arjona et al. 2008 and 2010). The existence and uniqueness of weak solutions for both the elastic-gravitational and viscoelastic-gravitational problem was demonstrated in Arjona et al. (2008 and 2014). The stabilization to solutions of the associated stationary system was proved in Arjona and Díaz (2007). Here we consider the internal source as response to the effect of a pressurized magma reservoir into a multilayered, elastic-gravitational and viscoelastic-gravitational earth model. We introduce the numerical analysis of a simplified steady elastic-gravitational model, solved by means of the finite element method. We also present some numerical tests in realistic situations that confirm the predictions of theoretical order of convergence. Finally, we describe the methodology for both the elastic-gravitational and the viscoelastic-gravitational models using 2D and 3D test examples performed with FreeFEM++.
Underestimation of nuclear fuel burnup – theory, demonstration and solution in numerical models
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Gajda Paweł
2016-01-01
Full Text Available Monte Carlo methodology provides reference statistical solution of neutron transport criticality problems of nuclear systems. Estimated reaction rates can be applied as an input to Bateman equations that govern isotopic evolution of reactor materials. Because statistical solution of Boltzmann equation is computationally expensive, it is in practice applied to time steps of limited length. In this paper we show that simple staircase step model leads to underprediction of numerical fuel burnup (Fissions per Initial Metal Atom – FIMA. Theoretical considerations indicates that this error is inversely proportional to the length of the time step and origins from the variation of heating per source neutron. The bias can be diminished by application of predictor-corrector step model. A set of burnup simulations with various step length and coupling schemes has been performed. SERPENT code version 1.17 has been applied to the model of a typical fuel assembly from Pressurized Water Reactor. In reference case FIMA reaches 6.24% that is equivalent to about 60 GWD/tHM of industrial burnup. The discrepancies up to 1% have been observed depending on time step model and theoretical predictions are consistent with numerical results. Conclusions presented in this paper are important for research and development concerning nuclear fuel cycle also in the context of Gen4 systems.
Numerical modeling of solute transport in deformable unsaturated layered soil
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Sheng Wu
2017-07-01
Full Text Available The effect of soil stratification was studied through numerical investigation based on the coupled model of solute transport in deformable unsaturated soil. The theoretical model implied two-way coupled excess pore pressure and soil deformation based on Biot's consolidation theory as well as a one-way coupled volatile pollutant concentration field developed from the advection-diffusion theory. Embedded in the model, the degree of saturation, fluid compressibility, self-weight of the soil matrix, porosity variance, longitudinal dispersion, and linear sorption were computed. Based on simulation results of a proposed three-layer landfill model using the finite element method, the multi-layer effects are discussed with regard to the hydraulic conductivity, shear modulus, degree of saturation, molecular diffusion coefficient, and thickness of each layer. Generally speaking, contaminants spread faster in a stratified field with a soft and highly permeable top layer; soil parameters of the top layer are more critical than the lower layers but controlling soil thicknesses will alter the results. This numerical investigation showed noticeable impacts of stratified soil properties on solute migration results, demonstrating the importance of correctly modeling layered soil instead of simply assuming the averaged properties across the soil profile.
On the numerical solution of the diffusion equation with a nonlocal boundary condition
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Dehghan Mehdi
2003-01-01
Full Text Available Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (MOL semidiscretization approach is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations (ODEs. The partial derivative with respect to the space variable is approximated by a second-order finite-difference approximation. The solution of the resulting system of first-order ODEs satisfies a recurrence relation which involves a matrix exponential function. Numerical techniques are developed by approximating the exponential matrix function in this recurrence relation. We use a partial fraction expansion to compute the matrix exponential function via Pade approximations, which is particularly useful in parallel processing. The algorithm is tested on a model problem from the literature.
Carmona, A.; Pérez-Segarra, C. D.; Lehmkuhl, O.; Oliva, A.
2012-11-01
The aim of this work is to provide numerical solutions for the fluid flow and the heat transfer generated in closed systems containing viscoplastic-type non-Newtonian fluids. A lid driven cavity (LDC) and a differentially heated cavity (DHC) are used as test cases. These numerical solutions can be an appropriate tool for verifying CFD codes which have been developed or adapted to deal with this kind of non-Newtonian fluids. In order to achieve this objective, an in-house CFD code has been implemented and correctly verified by the method of manufactured solutions and by some numerical solutions too. Furthermore, a high-performance CFD code (Termo Fluids S.L.) has been adapted and properly verified, by the corresponding numerical solutions, to deal with this kind of non-Newtonian fluids. The viscoplastic behaviour of certain non-Newtonian fluids will be generated from a viscous stress which has been defined by a potential-type rheological law. The pseudoplastic and dilatant behaviours will be studied. On this matter, the influence of different physical aspects on the numerical simulations will be analysed, e.g. different exponent values in the potential-type rheological law and different values of the non-dimensional numbers. Moreover, the influence of different numerical aspects on the numerical simulations will also be analysed, e.g. unstructured meshes, conservative numerical schemes and more efficient and parallel algorithms and solvers.
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Andranik Tsakanian
2012-05-01
Full Text Available In particle accelerators a preferred direction, the direction of motion, is well defined. If in a numerical calculation the (numerical dispersion in this direction is suppressed, a quite coarse mesh and moderate computational resources can be used to reach accurate results even for extremely short electron bunches. Several approaches have been proposed in the past decades to reduce the accumulated dispersion error in wakefield calculations for perfectly conducting structures. In this paper we extend the TE/TM splitting algorithm to a new hybrid scheme that allows for wakefield calculations in structures with walls of finite conductivity. The conductive boundary is modeled by one-dimensional wires connected to each boundary cell. A good agreement of the numerical simulations with analytical results and other numerical approaches is obtained.
Numerical solution of the helmholtz equation for the superellipsoid via the galerkin method
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Hy Dinh
2013-01-01
Full Text Available The objective of this work was to find the numerical solution of the Dirichlet problem for the Helmholtz equation for a smooth superellipsoid. The superellipsoid is a shape that is controlled by two parameters. There are some numerical issues in this type of an analysis; any integration method is affected by the wave number k, because of the oscillatory behavior of the fundamental solution. In this case we could only obtain good numerical results for super ellipsoids that were more shaped like super cones, which is a narrow range of super ellipsoids. The formula for these shapes was: $x=cos(xsin(y^{n},y=sin(xsin(y^{n},z=cos(y$ where $n$ varied from 0.5 to 4. The Helmholtz equation, which is the modified wave equation, is used in many scattering problems. This project was funded by NASA RI Space Grant for testing of the Dirichlet boundary condition for the shape of the superellipsoid. One practical value of all these computations can be getting a shape for the engine nacelles in a ray tracing the space shuttle. We are researching the feasibility of obtaining good convergence results for the superellipsoid surface. It was our view that smaller and lighter wave numbers would reduce computational costs associated with obtaining Galerkin coefficients. In addition, we hoped to significantly reduce the number of terms in the infinite series needed to modify the original integral equation, all of which were achieved in the analysis of the superellipsoid in a finite range. We used the Green's theorem to solve the integral equation for the boundary of the surface. Previously, multiple surfaces were used to test this method, such as the sphere, ellipsoid, and perturbation of the sphere, pseudosphere and the oval of Cassini Lin and Warnapala , Warnapala and Morgan .
Nuzzo, Stefano; Bolognesi, Paolo; Galea, Michael; Gerada, C.
2017-01-01
The equivalent circuit approach has been widely exploited for the theoretical analysis of electromagnetic devices. However, in the field of classical wound-field synchronous generators, the presence of the damper cage complicates the analysis of such devices and the accurate prediction of the inherent induced currents is still matter of ongoing research. 12Focus is given to the accurate prediction of the no-load voltage waveform, by implementing a hybrid analytical-numerical model for a speci...
Seyboldt, Christoph; Liewald, Mathias
2017-10-01
Current research activities at the Institute for Metal Forming Technology (IFU) of the University of Stuttgart are focusing on the manufacturing of hybrid components using semi-solid forming strategies. As part of the research project "Hybrid interaction during and after thixoforging of multi-material systems", which is founded by the German Research Foundation (DFG), a thixoforging process for producing hybrid components with cohesive metal-to-metal connections is developed. In this context, this paper deals with the numerical simulation of the inductive heating process of hybrid semi-finished materials, consisting of two different aluminium alloys. By reason of the skin effect that leads to inhomogeneous temperature distributions during inductive heating processes, the aluminium alloy with the higher melting point is thereby assembled in the outer side and the alloy with the lower melting point is assembled in the core of the semi-finished material. In this way, the graded heat distribution can be adapted to the used materialś flow properties that are heavily heat dependent. Without this graded heat distribution a proper forming process in the semi-solid state will not be possible. For numerically modelling the inductive heating system of the institute, a coupling of the magnetostatic and the thermal solver was realized by using Ansys Workbench. While the electromagnetic field and its associated heat production rate were solved in a frequency domain, the temperature development was solved in the time based domain. The numerical analysis showed that because of the high thermal conductivity of the aluminium, which leads to a rapid temperature equalization in the semi-finished material, the heating process has to be fast and with a high frequency for produce most heat in the outer region of the material. Finally, the obtained numerical results were validated with experimental heating tests.
Lucas, P.; Van Zuijlen, A.H.; Bijl, H.
2009-01-01
Mesh adaptation is a fairly established tool to obtain numerically accurate solutions for flow problems. Computational efficiency is, however, not always guaranteed for the adaptation strategies found in literature. Typically excessive mesh growth diminishes the potential efficiency gain. This
Bachevillier, Stefan
2016-10-01
After the use of highly efficient but expensive inorganic optical materials, solution-processable polymers and hybrids have drawn more and more interest. Our group have recently developed a novel polymer-based hybrid optical material from titanium oxide hydrate exhibiting an outstanding set of optical and material properties. Firstly, their low cost, processability and cross-linked states are particularly attractive for many applications. Moreover, a high refractive index can be repeatedly achieved while optical losses stays considerably low over the entire visible and near-infrared wavelength regime. Indeed, the formation of inorganic nanoparticles, usually present in nanocomposites, is avoided by a specific formulation process. Even more remarkably, the refractive index can be tuned by either changing the inorganic content, using different titanium precursors or via a low-temperature curing process. A part of our work is focused on the reliable optical characterization of these properties, in particular a microscope-based setup allowing in-situ measurement and sample mapping has been developed. Our efforts are also concentrated on various applications of these exceptional properties. This hybrid material is tailored for photonic devices, with a specific emphasis on the production of highly efficient solution processable Distributed Bragg Reflectors (DBR) and anti-reflection coatings. Furthermore, waveguides can be fabricated from thin films along with in-coupling and out-coupling structures. These light managements structures are particularly adapted to organic photovoltaic cells (OPVs) and light emitting diodes (OLEDs).
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Vasily Novozhilov
2011-10-01
Full Text Available Hybrid Propulsion is an attractive alternative to conventional liquid and solid rocket motors. This is an active area of research and technological developments. Potential wide application of Hybrid Engines opens the possibility for safer and more flexible space vehicle launching and manoeuvring. The present paper discusses fundamental combustion issues related to further development of Hybrid Rockets. The emphasis is made on the two aspects: (1 properties of potential polymeric fuels, and their modification, and (2 implementation of comprehensive CFD models for combustion in Hybrid Engines. Fundamentals of polymeric fuel combustion are discussed. Further, steps necessary to accurately describe their burning behaviour by means of CFD models are investigated. Final part of the paper presents results of preliminary CFD simulations of fuel burning process in Hybrid Engine using a simplified set-up.
Numerical solution of chemically reactive non-Newtonian fluid flow: Dual stratification
Rehman, Khalil Ur; Malik, M. Y.; Khan, Abid Ali; Zehra, Iffat; Zahri, Mostafa; Tahir, M.
2017-12-01
We have found that only a few attempts are available in the literature relatively to the tangent hyperbolic fluid flow induced by stretching cylindrical surfaces. In particular, temperature and concentration stratification effects have not been investigated until now with respect to the tangent hyperbolic fluid model. Therefore, we have considered the tangent hyperbolic fluid flow induced by an acutely inclined cylindrical surface in the presence of both temperature and concentration stratification effects. To be more specific, the fluid flow is attained with the no slip condition, which implies that the bulk motion of the fluid particles is the same as the stretching velocity of a cylindrical surface. Additionally, the flow field situation is manifested with heat generation, mixed convection and chemical reaction effects. The flow partial differential equations give a complete description of the present problem. Therefore, to trace out the solution, a set of suitable transformations is introduced to convert these equations into ordinary differential equations. In addition, a self-coded computational algorithm is executed to inspect the numerical solution of these reduced equations. The effect logs of the involved parameters are provided graphically. Furthermore, the variations of the physical quantities are examined and given with the aid of tables. It is observed that the fluid temperature is a decreasing function of the thermal stratification parameter and a similar trend is noticed for the concentration via the solutal stratification parameter.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
Constanda, Christian; Hamill, William
2016-01-01
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
To facilitate the validation of the numerical Method of Auxiliary Sources an analytical Method of Auxiliary Sources solution is derived in this paper. The Analytical solution is valid for transverse magnetic, and electric, plane wave scattering by circular impedance Cylinders, and it is derived...... of the numerical Method of Auxiliary Sources for a range of scattering configurations....... with their singularities at different positions away from the origin. The transformation necessitates a truncation of the wave transformation but the inaccuracy introduced hereby is shown to be negligible. The analytical Method of Auxiliary Sources solution is employed as a reference to investigate the accuracy...
Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach
Kiris, Cetin; Kwak, Dochan
1999-01-01
A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.
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M. Boumaza
2015-07-01
Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.
Solution-processed, nanostructured hybrid solar cells with broad spectral sensitivity and stability.
Zhou, Renjia; Zheng, Ying; Qian, Lei; Yang, Yixing; Holloway, Paul H; Xue, Jiangeng
2012-06-07
Hybrid organic-inorganic solar cells, as an alternative to all-organic solar cells, have received significant attention for their potential advantages in combining the solution-processability and versatility of organic materials with high charge mobility and environmental stability of inorganic semiconductors. Here we report efficient and air-stable hybrid organic-inorganic solar cells with broad spectral sensitivity based on a low-gap polymer poly[2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b']-dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT) and spherical CdSe nanoparticles. The solvents used for depositing the hybrid PCPDTBT:CdSe active layer were shown to strongly influence the film morphology, and subsequently the photovoltaic performance of the resulted solar cells. Appropriate post-deposition annealing of the hybrid film was also shown to improve the solar cell efficiency. The inclusion of a thin ZnO nanoparticle layer between the active layer and the metal cathode leads to a significant increase in device efficiency especially at long wavelengths, due to a combination of optical and electronic effects including more optimal light absorption in the active layer and elimination of unwanted hole leakage into the cathode. Overall, maximum power conversion efficiencies up to 3.7 ± 0.2% and spectral sensitivity extending above 800 nm were achieved in such PCPDTBT:CdSe nanosphere hybrid solar cells. Furthermore, the devices with a ZnO nanoparticle layer retained ∼70% of the original efficiency after storage under ambient laboratory conditions for over 60 days without any encapsulation.
Venturi, Daniele
2016-11-01
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics, quantum field theory and statistical physics. For example, in the context of fluid dynamics, the Hopf characteristic functional equation was deemed by Monin and Yaglom to be "the most compact formulation of the turbulence problem", which is the problem of determining the statistical properties of the velocity and pressure fields of Navier-Stokes equations given statistical information on the initial state. However, no effective numerical method has yet been developed to compute the solution to functional differential equations. In this talk I will provide a new perspective on this general problem, and discuss recent progresses in approximation theory for nonlinear functionals and functional equations. The proposed methods will be demonstrated through various examples.
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M. Hatami
2016-06-01
Full Text Available In this study, a simple and high accurate series-based method called Differential Transformation Method (DTM is used for solving the coupled nonlinear differential equations in fluids mechanic problems. The concept of the DTM is briefly introduced, and its application on two different cases, natural convection of a non-Newtonian nanofluid between two vertical plates and Newtonian nanofluid flow between two horizontal plates, has been studied. DTM results are compared with those obtained by a numerical solution (Fourth-order Runge–Kutta to show the accuracy of the proposed method. Results reveal that DTM is very effective and convenient which can achieve more reliable results compared to other analytical methods in solving some engineering and sciences problems.
Riemannian Gradient Algorithm for the Numerical Solution of Linear Matrix Equations
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Xiaomin Duan
2014-01-01
Full Text Available A Riemannian gradient algorithm based on geometric structures of a manifold consisting of all positive definite matrices is proposed to calculate the numerical solution of the linear matrix equation Q=X+∑i=1mAiTXAi. In this algorithm, the geodesic distance on the curved Riemannian manifold is taken as an objective function and the geodesic curve is treated as the convergence path. Also the optimal variable step sizes corresponding to the minimum value of the objective function are provided in order to improve the convergence speed. Furthermore, the convergence speed of the Riemannian gradient algorithm is compared with that of the traditional conjugate gradient method in two simulation examples. It is found that the convergence speed of the provided algorithm is faster than that of the conjugate gradient method.
Numerical simulation on vapor absorption by wavy lithium bromide aqueous solution films
Bo, Shoushi; Ma, Xuehu; Chen, Hongxia; Lan, Zhong
2011-12-01
Numerical simulation has been made on heat and mass transfer of vapor absorption by wavy lithium bromide aqueous solution films. The velocity fields and interface positions are obtained by VOF model. Solitary waves are generated by periodically disturbed inflow boundary. Based on these, the temperature and concentration fields are obtained with a stationary interface shape. The effect of solitary waves on the heat and mass transfer across the film is investigated. It is shown that due to the mixing of circulation and stretch of large film thickness, the gradient of concentration and absorption rate decrease for solitary wave region. The region of capillary waves shows a significant amount of absorption enhancement. The percentage of absorption for the different regions is quantified.
Zhu, Shichen; Yu, Xiaoyue; Xiong, Shanbai; Liu, Ru; Gu, Zhipeng; You, Juan; Yin, Tao; Hu, Yang
2017-09-01
The elaboration of the rheological behaviors of alginate dialdehyde (ADA) crosslinked collagen solutions, along with the quantitative analysis via numerical models contribute to the controllable design of ADA crosslinked solution system's fluid mechanics performance during manufacturing process for collagen biomaterials. In the present work, steady shear flow, dynamical viscoelasticity, creep-recovery, thixotropy tests were performed to characterize the rheological behaviors of the collagen solutions incorporating of ADA from the different aspects and fitted with corresponding numerical models. It was found that pseudoplastic properties of all samples enhanced with increasing amounts of ADA, which was confirmed by the parameters calculated from the Ostwald-de Waele model, Carreau and Cross model, for instance, the non-Newtonian index (n) decreased from 0.786 to 0.201 and a great increase by 280 times in value of viscosity index (K) was obtained from Ostwald-de Waele model. The forth-mode Leonov model was selected to fit all dynamic modulus-frequency curves due to its higher fitting precision (R 2 >0.99). It could be found that the values of correlation shear viscosity (η k ) increased and the values of relaxation time (θ k ) decreased with increasing ADA at the fixed k value, suggesting that the incorporation of ADA accelerated the transformation of the collagen solutions from liquid-like to gel-like state due to more formation of CN linkages between aldehyde groups and lysine residues. Also, the curves of creep and recovery phase of the native and crosslinked collagen solutions were simulated well using Burger model and a semi-empirical model, respectively. The ability to resist to deformation and elasticity strengthened for the samples with higher amounts of ADA, accompanied with the important fact that compliance value (J 50 ) decreased from 56.317Pa -1 to 2.135Pa -1 and the recovery percentage (R creep ) increased from 2.651% to 28.217%. Finally, it was found
Advanced Numerical Methods for Three-Dimensional Parallel Hybrid MHD/PIC
National Research Council Canada - National Science Library
McCrory, Robert
1996-01-01
.... The main conclusion of our study is that computationally efficient and physically sound description of nonsteady plasmas typical for these applications is possible using the advanced hybrid MHD/PIC...
Bahşı, Ayşe Kurt; Yalçınbaş, Salih
2016-01-01
In this study, the Fibonacci collocation method based on the Fibonacci polynomials are presented to solve for the fractional diffusion equations with variable coefficients. The fractional derivatives are described in the Caputo sense. This method is derived by expanding the approximate solution with Fibonacci polynomials. Using this method of the fractional derivative this equation can be reduced to a set of linear algebraic equations. Also, an error estimation algorithm which is based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation algorithm. If the exact solution of the problem is not known, the absolute error function of the problems can be approximately computed by using the Fibonacci polynomial solution. By using this error estimation function, we can find improved solutions which are more efficient than direct numerical solutions. Numerical examples, figures, tables are comparisons have been presented to show efficiency and usable of proposed method.
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Kevin G McCracken
Full Text Available Interspecific hybridization is common in plants and animals, particularly in waterfowl (Anatidae. One factor shown to contribute to hybridization is restricted mate choice, which can occur when two species occur in sympatry but one is rare. The Hubbs principle, or "desperation hypothesis," states that under such circumstances the rarer species is more likely to mate with heterospecifics. Here we report interspecific hybridization between two waterfowl species that coexist in broad sympatry and mixed flocks throughout southern South America. Speckled teal (Anas flavirostris and yellow-billed pintails (Anas georgica are abundant in continental South America, but in the Falkland Islands speckled teal outnumber yellow-billed pintails approximately ten to one. Using eight genetic loci (mtDNA and 7 nuclear introns coupled with Bayesian assignment tests and relatedness analysis, we identified a speckled teal x yellow-billed pintail F(1 hybrid female and her duckling sired by a male speckled teal. Although our sample in the Falkland Islands was small, we failed to identify unequivocal evidence of hybridization or introgression in a much larger sample from Argentina using a three-population "isolation with migration" coalescent analysis. While additional data are needed to determine if this event in the Falkland Islands was a rare singular occurrence, our results provide further support for the "desperation hypothesis," which states that scarcity in one population and abundance of another will often lead to hybridization.
Zhang, Bo; Chen, Tianning; Zhao, Yuyuan; Zhang, Weiyong; Zhu, Jian
2012-09-01
On the basis of the work of Wilson et al. [J. Acoust. Soc. Am. 84, 350-359 (1988)], a more exact numerical approach was constructed for predicting the nonlinear sound propagation and absorption properties of rigid porous media at high sound pressure levels. The numerical solution was validated by the experimental results for sintered fibrous porous steel samples and its predictions were compared with the numerical solution of Wilson et al. An approximate analytical solution was further put forward for the normalized surface acoustic admittance of rigid air-saturated porous materials with infinite thickness, based on the wave perturbation method developed by Lambert and McIntosh [J. Acoust. Soc. Am. 88, 1950-1959 (1990)]. Comparisons were made with the numerical results.
Bhattacharya, Amitabh; Kesarkar, Tejas
2016-10-01
A combination of finite difference (FD) and boundary integral (BI) methods is used to formulate an efficient solver for simulating unsteady Stokes flow around particles. The two-dimensional (2D) unsteady Stokes equation is being solved on a Cartesian grid using a second order FD method, while the 2D steady Stokes equation is being solved near the particle using BI method. The two methods are coupled within the viscous boundary layer, a few FD grid cells away from the particle, where solutions from both FD and BI methods are valid. We demonstrate that this hybrid method can be used to accurately solve for the flow around particles with irregular shapes, even though radius of curvature of the particle surface is not resolved by the FD grid. For dilute particle concentrations, we construct a virtual envelope around each particle and solve the BI problem for the flow field located between the envelope and the particle. The BI solver provides velocity boundary condition to the FD solver at "boundary" nodes located on the FD grid, adjacent to the particles, while the FD solver provides the velocity boundary condition to the BI solver at points located on the envelope. The coupling between FD method and BI method is implicit at every time step. This method allows us to formulate an O(N) scheme for dilute suspensions, where N is the number of particles. For semidilute suspensions, where particles may cluster, an envelope formation method has been formulated and implemented, which enables solving the BI problem for each individual particle cluster, allowing efficient simulation of hydrodynamic interaction between particles even when they are in close proximity. The method has been validated against analytical results for flow around a periodic array of cylinders and for Jeffrey orbit of a moving ellipse in shear flow. Simulation of multiple force-free irregular shaped particles in the presence of shear in a 2D slit flow has been conducted to demonstrate the robustness of
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Hai Zhang
2017-01-01
Full Text Available This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractional-order hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the U-layer and V-layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.
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Nilson C. Roberty
2011-01-01
Full Text Available We introduce algorithms marching over a polygonal mesh with elements consistent with the propagation directions of the particle (radiation flux. The decision for adopting this kind of mesh to solve the one-speed Boltzmann transport equation is due to characteristics of the domain of the transport operator which controls derivatives only in the direction of propagation of the particles (radiation flux in the absorbing and scattering media. This a priori adaptivity has the advantages that it formulates a consistent scheme which makes appropriate the application of the Lax equivalence theorem framework to the problem. In this work, we present the main functional spaces involved in the formalism and a description of the algorithms for the mesh generation and the transport equation solution. Some numerical examples related to the solution of a transmission problem in a high-contrast model with absorption and scattering are presented. Also, a comparison with benchmarks problems for source and reactor criticality simulations shows the compatibility between calculations with the algorithms proposed here and theoretical results.
Nadeem, Sohail; Masood, Sadaf; Mehmood, Rashid; Sadiq, Muhammad Adil
2015-01-01
The present analysis deals with flow and heat transfer aspects of a micropolar nanofluid between two horizontal parallel plates in a rotating system. The governing partial differential equations for momentum, energy, micro rotation and nano-particles concentration are presented. Similarity transformations are utilized to convert the system of partial differential equations into system of ordinary differential equations. The reduced equations are solved analytically with the help of optimal homotopy analysis method (OHAM). Analytical solutions for velocity, temperature, micro-rotation and concentration profiles are expressed graphically against various emerging physical parameters. Physical quantities of interest such as skin friction co-efficient, local heat and local mass fluxes are also computed both analytically and numerically through mid-point integration scheme. It is found that both the solutions are in excellent agreement. Local skin friction coefficient is found to be higher for the case of strong concentration i.e. n=0, as compared to the case of weak concentration n=0.50. Influence of strong and weak concentration on Nusselt and Sherwood number appear to be similar in a quantitative sense.
New numerical methods for open-loop and feedback solutions to dynamic optimization problems
Ghosh, Pradipto
The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development
The Numerical Solutions of a Two-Dimensional Space-Time Riesz-Caputo Fractional Diffusion Equation
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Necati Ozdemir
2011-07-01
Full Text Available This paper is concerned with the numerical solutions of a two-dimensional space-timefractional differential equation used to model the dynamic properties of complex systems governedby anomalous diffusion. The space-time fractional anomalous diffusion equation is definedby replacing the second order space and the first order time derivatives with Riesz and Caputooperators, respectively. Using the Laplace and Fourier transforms, a general representation ofanalytical solution is obtained in terms of the Mittag-Leffler function. Gr¨unwald-Letnikov (GLapproximation is also used to find numerical solution of the problem. Finally, simulation resultsfor two examples illustrate the comparison of the analytical and numerical solutions and alsovalidity of the GL approach to this problem.
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Bo Wang
2018-02-01
Full Text Available This paper presents the numerical investigation on the seismic performance of a steel–concrete hybrid structure consisting of reinforced concrete (RC tubular columns and steel braced truss with A-shaped steel frames, which is a novel supporting structural system to house air-cooled condensers (ACC in large-capacity thermal power plants (TPPs. First, the finite element (FE modeling approach for this hybrid structure using the software ABAQUS was validated by a range of pseudo-dynamic tests (PDTs performed on a 1/8-scaled sub-structure. The failure process, lateral displacement responses, changing rules of dynamic characteristic parameters and lateral stiffness with increase of peak ground acceleration (PGA were presented here. Then, nonlinear time-history analysis of the prototype structure was carried out. The dynamic characteristics, base shear force, lateral deformation capacity, stiffness deterioration and damage characteristics were investigated. Despite the structural complexity and irregularity, both experimental and numerical results indicate that the overall seismic performance of this steel–concrete hybrid supporting structure meets the seismic design requirements with respect to the high-intensity earthquakes.
AMINO AND MERCAPTO-SILICA HYBRID FOR Cd(II ADSORPTION IN AQUEOUS SOLUTION
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Buhani Buhani
2010-06-01
Full Text Available Modification of silica gel with 3-aminopropyltrimethoxysilane and 3-mercaptopropyltrimethoxysilane through sol-gel technique producing amino-silica hybrid (HAS and mercapto-silica hybrid (HMS, respectively, has been carried out using tetraethylorthosilicate (TEOS as silica source. The adsorbents were characterized using infrared spectroscopy (IR, and X-ray energy dispersion spectroscopy (EDX. Adsorption of Cd(II individually as well as its binary mixture with Ni(II, Cu(II, and Zn(II in solution was performed in a batch system. Adsorption capacities of Cd(II ion on adsorbent of silica gel (SG, HAS, and HMS are 86.7, 256.4 and 319.5 μmol/g with the adsorption energies are 24.60, 22.61 and 23.15 kJ/mol, respectively. Selectivity coefficient (α of Cd(II ion toward combination of Cd(II/Ni(II, Cd(II/Cu(II, and Cd(II/Zn(II ions on HAS adsorbent is relatively smaller than those on HMS adsorbent which has α > 1. Keywords: adsorption, amino-silica hybrid, mercapto-silica
Rahman, M. Saifur; Anower, Md. Shamim; Hasan, Md. Rabiul; Hossain, Md. Biplob; Haque, Md. Ismail
2017-08-01
We demonstrate a highly sensitive Au-MoS2-Graphene based hybrid surface plasmon resonance (SPR) biosensor for the detection of DNA hybridization. The performance parameters of the proposed sensor are investigated in terms of sensitivity, detection accuracy and quality factor at operating wavelength of 633 nm. We observed in the numerical study that sensitivity can be greatly increased by adding MoS2 layer in the middle of a Graphene-on-Au layer. It is shown that by using single layer of MoS2 in between gold and graphene layer, the proposed biosensor exhibits simultaneously high sensitivity of 87.8 deg/RIU, high detection accuracy of 1.28 and quality factor of 17.56 with gold layer thickness of 50 nm. This increased performance is due to the absorption ability and optical characteristics of graphene biomolecules and high fluorescence quenching ability of MoS2. On the basis of changing in SPR angle and minimum reflectance, the proposed sensor can sense nucleotides bonding happened between double-stranded DNA (dsDNA) helix structures. Therefore, this sensor can successfully detect the hybridization of target DNAs to the probe DNAs pre-immobilized on the Au-MoS2-Graphene hybrid with capability of distinguishing single-base mismatch.
Markos, Christos
2016-08-19
The possibility to combine silica photonic crystal fiber (PCF) as low-loss platform with advanced functional materials, offers an enormous range of choices for the development of fiber-based tunable devices. Here, we report a tunable hybrid silica PCF with integrated As2S3 glass nanolayers inside the air-capillaries of the fiber based on a solution-processed glass approach. The deposited high-index layers revealed antiresonant transmission windows from ~500 nm up to ~1300 nm. We experimentally demonstrate for the first time the possibility to thermally-tune the revealed antiresonances by taking advantage the high thermo-optic coefficient of the solution-processed nanolayers. Two different hybrid fiber structures, with core diameter 10 and 5 μm, were developed and characterized using a supercontinuum source. The maximum sensitivity was measured to be as high as 3.6 nm/°C at 1300 nm. The proposed fiber device could potentially constitute an efficient route towards realization of monolithic tunable fiber filters or sensing elements.
Optimal Solution for VLSI Physical Design Automation Using Hybrid Genetic Algorithm
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I. Hameem Shanavas
2014-01-01
Full Text Available In Optimization of VLSI Physical Design, area minimization and interconnect length minimization is an important objective in physical design automation of very large scale integration chips. The objective of minimizing the area and interconnect length would scale down the size of integrated chips. To meet the above objective, it is necessary to find an optimal solution for physical design components like partitioning, floorplanning, placement, and routing. This work helps to perform the optimization of the benchmark circuits with the above said components of physical design using hierarchical approach of evolutionary algorithms. The goal of minimizing the delay in partitioning, minimizing the silicon area in floorplanning, minimizing the layout area in placement, minimizing the wirelength in routing has indefinite influence on other criteria like power, clock, speed, cost, and so forth. Hybrid evolutionary algorithm is applied on each of its phases to achieve the objective. Because evolutionary algorithm that includes one or many local search steps within its evolutionary cycles to obtain the minimization of area and interconnect length. This approach combines a hierarchical design like genetic algorithm and simulated annealing to attain the objective. This hybrid approach can quickly produce optimal solutions for the popular benchmarks.
Bimetallic AgCu/Cu2O hybrid for the synergetic adsorption of iodide from solution.
Mao, Ping; Liu, Ying; Liu, Xiaodong; Wang, Yuechan; Liang, Jie; Zhou, Qihang; Dai, Yuexuan; Jiao, Yan; Chen, Shouwen; Yang, Yi
2017-08-01
To further improve the capacity of Cu 2 O to absorb I - anions from solution, and to understand the difference between the adsorption mechanisms of Ag/Cu 2 O and Cu/Cu 2 O adsorbents, bimetallic AgCu was doped into Cu 2 O through a facile solvothermal route. Samples were characterized and employed to adsorb I - anions under different experimental conditions. The results show that the Cu content can be tuned by adding different volumes of Ag sols. After doping bimetallic AgCu, the adsorption capacity of the samples can be increased from 0.02 mmol g -1 to 0.52 mmol g -1 . Moreover, the optimal adsorption is reached within only 240 min. Meanwhile, the difference between the adsorption mechanisms of Ag/Cu 2 O and Cu/Cu 2 O adsorbents was verified, and the cooperative adsorption mechanism of the AgCu/Cu 2 O hybrid was proposed and verified. In addition, the AgCu/Cu 2 O hybrid showed excellent selectivity, e.g., its adsorption efficiencies are 85.1%, 81.9%, 85.9% and 85.7% in the presence of the Cl - , CO 3 2- , SO 4 2- and NO 3 - competitive anions, respectively. Furthermore, the AgCu/Cu 2 O hybrid can worked well in other harsh environments (e.g., acidic, alkaline and seawater environments). Therefore, this study is expected to promote the development of Cu 2 O into a highly efficient adsorbent for the removal of iodide from solution. Copyright © 2017 Elsevier Ltd. All rights reserved.
Mazar Atabaki, M.; Nikodinovski, M.; Chenier, P.; Ma, J.; Liu, W.; Kovacevic, R.
2014-07-01
In the present investigation, a numerical finite element model was developed to simulate the hybrid laser arc welding of different aluminum alloys, namely 5××× to 6××× series. The numerical simulation has been considered two double-ellipsoidal heat sources for the gas metal arc welding and laser welding. The offset distance of the metal arc welding and laser showed a significant effect on the molten pool geometry, the heat distribution and penetration depth during the welding process. It was confirmed that when the offset distance is within the critical distance the laser and arc share the molten pool and specific amount of penetration and dilution can be achieved. The models and experiments show that the off-distance between the two heat sources and shoulder width have considerable influence on the penetration depth and appearance of the weld beads. The experiments also indicate that the laser power, arc voltage and type of the filler metal can effectively determine the final properties of the bonds, specifically the bead appearance and microhardness of the joints. The experiments verified the numerical simulation as the thermocouples assist to comprehend the amount of heat distribution on the T-joint coupons. The role of the welding parameters on the mechanism of the hybrid laser welding of the aluminum alloys was also discussed.
Zhang, Shuai; Hu, Fan; Wang, Donghui; Okolo, N. Patrick; Zhang, Weihua
2017-07-01
Numerical simulations on processes within a hybrid rocket motor were conducted in the past, where most of these simulations carried out majorly focused on steady state analysis. Solid fuel regression rate strongly depends on complicated physicochemical processes and internal fluid dynamic behavior within the rocket motor, which changes with both space and time during its operation, and are therefore more unsteady in characteristics. Numerical simulations on the unsteady operational processes of N2O/HTPB hybrid rocket motor with and without diaphragm are conducted within this research paper. A numerical model is established based on two dimensional axisymmetric unsteady Navier-Stokes equations having turbulence, combustion and coupled gas/solid phase formulations. Discrete phase model is used to simulate injection and vaporization of the liquid oxidizer. A dynamic mesh technique is applied to the non-uniform regression of fuel grain, while results of unsteady flow field, variation of regression rate distribution with time, regression process of burning surface and internal ballistics are all obtained. Due to presence of eddy flow, the diaphragm increases regression rate further downstream. Peak regression rates are observed close to flow reattachment regions, while these peak values decrease gradually, and peak position shift further downstream with time advancement. Motor performance is analyzed accordingly, and it is noticed that the case with diaphragm included results in combustion efficiency and specific impulse efficiency increase of roughly 10%, and ground thrust increase of 17.8%.
Thompson, J. F.; Mastin, C. W.; Thames, F. C.; Shanks, S. P.
1975-01-01
A procedure for numerical solution of the time-dependent, two-dimensional incompressible Navier-Stokes equations that can treat the unsteady laminar flow about bodies of arbitrary shape, such as two-dimensional airfoils, multiple airfoils, and submerged hydrofoils, as naturally as it can deal with the flow about simple bodies. The solution is based on a method of automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multiconnected region containing any number of arbitrarily shaped bodies. The curvilinear coordinates are generated as the solution of two elliptical partial differential equations with Dirichlet boundary conditions, one coordinate being specified to be constant on each of the boundaries, and a distribution of the other being specified along the boundaries. The solution compares excellently with the Blasius boundary layer solution for the flow past a semiinfinite flat plate.
A novel hybrid algorithm of GSA with Kepler algorithm for numerical optimization
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Soroor Sarafrazi
2015-07-01
Full Text Available It is now well recognized that pure algorithms can be promisingly improved by hybridization with other techniques. One of the relatively new metaheuristic algorithms is Gravitational Search Algorithm (GSA which is based on the Newton laws. In this paper, to enhance the performance of GSA, a novel algorithm called “Kepler”, inspired by the astrophysics, is introduced. The Kepler algorithm is based on the principle of the first Kepler law. The hybridization of GSA and Kepler algorithm is an efficient approach to provide much stronger specialization in intensification and/or diversification. The performance of GSA–Kepler is evaluated by applying it to 14 benchmark functions with 20–1000 dimensions and the optimal approximation of linear system as a practical optimization problem. The results obtained reveal that the proposed hybrid algorithm is robust enough to optimize the benchmark functions and practical optimization problems.
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Qicheng Meng
2016-04-01
Full Text Available A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system. The solution corrects an error by Mirie and Su (1984. A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam. Various analytical solutions, including the first-order to third-order KdV solutions, the eKdV solution and the MCC solution, have been used to initialise the flow fields in the CFD simulations of internal solitary waves. Two groups including 11 numerical cases have been carried out. In the same group, the initial wave amplitudes are the same but the implemented analytical solutions are different. The simulated wave profiles at different moments have been presented. The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively. It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases. The finding is significant for the further simulations involving internal solitary waves.
An Effective Hybrid Firefly Algorithm with Harmony Search for Global Numerical Optimization
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Lihong Guo
2013-01-01
Full Text Available A hybrid metaheuristic approach by hybridizing harmony search (HS and firefly algorithm (FA, namely, HS/FA, is proposed to solve function optimization. In HS/FA, the exploration of HS and the exploitation of FA are fully exerted, so HS/FA has a faster convergence speed than HS and FA. Also, top fireflies scheme is introduced to reduce running time, and HS is utilized to mutate between fireflies when updating fireflies. The HS/FA method is verified by various benchmarks. From the experiments, the implementation of HS/FA is better than the standard FA and other eight optimization methods.
Energy Technology Data Exchange (ETDEWEB)
Hernandez M, N. [CFE, Carretera Cardel-Nautla Km. 43.5, 91680 Veracruz (Mexico); Alonso V, G.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: nhmiranda@mexico.com
2003-07-01
In 1979, Hennart and collaborators applied several schemes of classic finite element in the numerical solution of the diffusion equations in X Y geometry and stationary state. Almost two decades then, in 1996, himself and other collaborators carried out a similar work but using nodal schemes type finite element. Continuing in this last direction, in this work a group it is described a set of several Hybrid Nodal schemes denominated (NH) as well as their application to solve the diffusion equations in multigroup in stationary state and X Y geometry. The term hybrid nodal it means that such schemes interpolate not only Legendre moments of face and of cell but also the values of the scalar flow of neutrons in the four corners of each cell or element of the spatial discretization of the domain of interest. All the schemes here considered are polynomials like they were it their predecessors. Particularly, its have developed and applied eight different hybrid nodal schemes that its are very nearby related with those developed by Hennart and collaborators in the past. It is treated of schemes in those that nevertheless that decreases the number of interpolation parameters it is conserved the accurate in relation to the bi-quadratic and bi-cubic schemes. Of these eight, three were described and applied in a previous work. It is the bi-lineal classic scheme as well as the hybrid nodal schemes, bi-quadratic and bi-cubic for that here only are described the other 5 hybrid nodal schemes although they are provided numerical results for several test problems with all them. (Author)
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Edris Yousefi Rad
2017-08-01
Full Text Available In the present research, considering the importance of desirable steam turbine design, improvement of numerical modeling of steam two-phase flows in convergent and divergent channels and the blades of transonic steam turbines has been targeted. The first novelty of this research is the innovative use of combined Convective Upstream Pressure Splitting (CUSP and scalar methods to update the flow properties at each calculation point. In other words, each property (density, temperature, pressure and velocity at each calculation point can be computed from either the CUSP or scalar method, depending on the least deviation criterion. For this reason this innovative method is named “hybrid method”. The next novelty of this research is the use of an inverse method alongside the proposed hybrid method to find the amount of the important parameter z in the CUSP method, which is herein referred to as “CUSP’s convergence parameter”. Using a relatively simple computational grid, firstly, five cases with similar conditions to those of the main cases under study in this research with available experimental data were used to obtain the value of z by the Levenberg-Marquardt inverse method. With this innovation, first, an optimum value of z = 2.667 was obtained using the inverse method and then directly used for the main cases considered in the research. Given that the aim is to investigate the two-dimensional, steady state, inviscid and adiabatic modeling of steam nucleating flows in three different nozzle and turbine blade geometries, flow simulation was performed using a relatively simple mesh and the innovative proposed hybrid method (scalar + CUSP, with the desired value of z = 2.667 . A comparison between the results of the hybrid modeling of the three main cases with experimental data showed a very good agreement, even within shock zones, including the condensation shock region, revealing the efficiency of this numerical modeling method innovation
A hybrid solution approach for a multi-objective closed-loop logistics network under uncertainty
Mehrbod, Mehrdad; Tu, Nan; Miao, Lixin
2014-09-01
The design of closed-loop logistics (forward and reverse logistics) has attracted growing attention with the stringent pressures of customer expectations, environmental concerns and economic factors. This paper considers a multi-product, multi-period and multi-objective closed-loop logistics network model with regard to facility expansion as a facility location-allocation problem, which more closely approximates real-world conditions. A multi-objective mixed integer nonlinear programming formulation is linearized by defining new variables and adding new constraints to the model. By considering the aforementioned model under uncertainty, this paper develops a hybrid solution approach by combining an interactive fuzzy goal programming approach and robust counterpart optimization based on three well-known robust counterpart optimization formulations. Finally, this paper compares the results of the three formulations using different test scenarios and parameter-sensitive analysis in terms of the quality of the final solution, CPU time, the level of conservatism, the degree of closeness to the ideal solution, the degree of balance involved in developing a compromise solution, and satisfaction degree.
Schöpfer, Martin; Lehner, Florian; Grasemann, Bernhard; Kaserer, Klemens; Hinsch, Ralph
2017-04-01
John G. Ramsay's sketch of structures developed in a layer progressively folded and deformed by tangential longitudinal strain (Figure 7-65 in Folding and Fracturing of Rocks) and the associated strain pattern analysis have been reproduced in many monographs on Structural Geology and are referred to in numerous publications. Although the origin of outer-arc extension fractures is well-understood and documented in many natural examples, geomechanical factors controlling their (finite or saturation) spacing are hitherto unexplored. This study investigates the formation of bending-induced fractures during constant-curvature forced folding using Distinct Element Method (DEM) numerical modelling. The DEM model comprises a central brittle layer embedded within weaker (low modulus) elastic layers; the layer interfaces are frictionless (free slip). Folding of this three-layer system is enforced by a velocity boundary condition at the model base, while a constant overburden pressure is maintained at the model top. The models illustrate several key stages of fracture array development: (i) Prior to the onset of fracture, the neutral surface is located midway between the layer boundaries; (ii) A first set of regularly spaced fractures develops once the tensile stress in the outer-arc equals the tensile strength of the layer. Since the layer boundaries are frictionless, these bending-induced fractures propagate through the entire layer; (iii) After the appearance of the first fracture set, the rate of fracture formation decreases rapidly and so-called infill fractures develop approximately midway between two existing fractures (sequential infilling); (iv) Eventually no new fractures form, irrespective of any further increase in fold curvature (fracture saturation). Analysis of the interfacial normal stress distributions suggests that at saturation the fracture-bound blocks are subjected to a loading condition similar to three-point bending. Using classical beam theory an
Numerical Investigations of Vadose Zone Transport of Saturated Sodium Thiosulfate Solutions
White, M. D.; Ward, A. L.
2001-12-01
Compared with water, hypersaline liquid wastes ([NaNO3] > 10 N) from the reduction-oxidation (REDOX) process at the Hanford site have elevated viscosity (μ > 1.2 cP), density (ρ > 1.4 gm/cm3), and surface tension (σ > 100 dyn/cm). Such liquids have infiltrated into the vadose zone at Hanford from leaking underground storage tanks. The migration behavior of saturated or hypersaline salt solutions through unsaturated soils is largely unknown. Laboratory tests with tank-waste simulants suggest that the elevated density, viscosity, and surface tension properties of these liquids can influence the wetting front behavior, altering its shape and migration rate. Conditions under which these mechanisms are active in the field and the extent to which they contribute to transport through the vadose zone are largely unknown, making it impossible to accurately predict the post-leak distribution of these fluids in the field. To investigate the effects of fluid properties on subsurface migration of hypersaline saline solutions, numerical simulations were conducted of a field-scale, tank-leak experiment. The field experiments consisted of five 4000-L injections, at a depth of 5 m, of saturated sodium thiosulfate brine (used as a surrogate for REDOX type wastes) over a 5-week period, followed by three 4000-L injections of Columbia River water. Pre-test modeling of river water injections at this Hanford field site predicted significant lateral spreading of the moisture plume and were confirmed by geophysical logging. A series of three-dimensional, multifluid (i.e., aqueous and gas phases) numerical simulations were conducted that systematically considered the effects of elevated density, viscosity, and surface tension, and reduced vapor pressure on vadose-zone transport. Hydrologic properties were determined from cores collected at the field site and calibrated using river-water injection experiments. Isothermal conditions were assumed for the simulations, however, the effects of
Kudryavtsev, Alexey N.; Kashkovsky, Alexander V.; Borisov, Semyon P.; Shershnev, Anton A.
2017-10-01
In the present work a computer code RCFS for numerical simulation of chemically reacting compressible flows on hybrid CPU/GPU supercomputers is developed. It solves 3D unsteady Euler equations for multispecies chemically reacting flows in general curvilinear coordinates using shock-capturing TVD schemes. Time advancement is carried out using the explicit Runge-Kutta TVD schemes. Program implementation uses CUDA application programming interface to perform GPU computations. Data between GPUs is distributed via domain decomposition technique. The developed code is verified on the number of test cases including supersonic flow over a cylinder.
On the formation, growth, and shapes of solution pipes - insights from numerical modeling
Szymczak, Piotr; Tredak, Hanna; Upadhyay, Virat; Kondratiuk, Paweł; Ladd, Anthony J. C.
2015-04-01
Cylindrical, vertical structures called solution pipes are a characteristic feature of epikarst, encountered in different parts of the world, both in relatively cold areas such as England and Poland (where their formation is linked to glacial processes) [1] and in coastal areas in tropical or subtropical climate (Bermuda, Australia, South Africa, Caribbean, Mediterranean) [2,3]. They are invariably associated with weakly cemented, porous limestones and relatively high groundwater fluxes. Many of them develop under the colluvial sandy cover and contain the fill of clayey silt. Although it is widely accepted that they are solutional in origin, the exact mechanism by which the flow becomes focused is still under debate. The hypotheses include the concentration of acidified water around stems and roots of plants, or the presence of pre-existing fractures or steeply dipping bedding planes, which would determine the points of entry for the focused groundwater flows. However, there are field sites where neither of this mechanisms was apparently at play and yet the pipes are formed in large quantities [1]. In this communication we show that the systems of solution pipes can develop spontaneously in nearly uniform matrix due to the reactive-infiltration instability: a homogeneous porous matrix is unstable with respect to small variations in local permeability; regions of high permeability dissolve faster because of enhanced transport of reactants, which leads to increased rippling of the front. This leads to the formation of a system of solution pipes which then advance into the matrix. We study this process numerically, by a combination of 2d- and 3d-simulations, solving the coupled flow and transport equations at the Darcy scale. The relative simplicity of this system (pipes developing in a uniform porous matrix, without any pre-existing structure) makes it very attractive from the modeling standpoint. We quantify the factors which control the pipe diameters and the
Yao, Lingxing; Mori, Yoichiro
2017-12-01
Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.
Evaluate the accuracy of the numerical solution of hydrogeological problems of mass transfer
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Yevhrashkina G.P.
2014-12-01
Full Text Available In the hydrogeological task on quantifying pollution of aquifers the error are starting add up with moment organization of regime observation network as a source of information on the pollution of groundwater in order to evaluate migration options for future prognosis calculations. Optimum element regime observation network should consist of three drill holes on the groundwater flow at equal distances from one another and transversely to the flow of the three drill holes, and at equal distances. If the target of observation drill holes coincides with the stream line on which will then be decided by direct migration task, the error will be minimal. The theoretical basis and results of numerical experiments to assess the accuracy of direct predictive tasks planned migration of groundwater in the area of full water saturation. For the vadose zone, we consider problems of vertical salt transport moisture. All studies were performed by comparing the results of fundamental and approximate solutions in a wide range of characteristics of the processes, which are discussed in relation to ecological and hydrogeological conditions of mining regions on the example of the Western Donbass.
Uncoupled continuous-time random walk model: analytical and numerical solutions.
Fa, Kwok Sau
2014-05-01
Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
Uncoupled continuous-time random walk model: Analytical and numerical solutions
Fa, Kwok Sau
2014-05-01
Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
Pandey, Rishi Kumar; Mishra, Hradyesh Kumar
2017-11-01
In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.
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Soyeon Park
2015-01-01
Full Text Available Hydroxyapatite (HAp/chitosan composites were prepared by a coprecipitation method, dropping a mixture of chitosan solution and phosphoric acid solution into a calcium hydroxide solution. Using the HAp/chitosan composites prepared, HAp/chitosan hybrid fibers with various HAp contents were prepared by a wet spinning method. X-ray diffraction and scanning electron microscopy analyses revealed that HAp particles were coated onto the surface of the fiber, and the surface roughness increased with increasing the HAp contents in the fiber. In order to evaluate the heavy metal removal characteristics of the HAp/chitosan hybrid fiber, adsorption tests were conducted and the results were compared with those of bare chitosan fibers. The results showed better performance in heavy metal ion removal for the HAp/chitosan hybrid fiber than the chitosan fiber. As the HAp content in the hybrid fiber increased, the removal efficiency of heavy metal ions also increased due to the increase of the specific surface area of the HAp/chitosan hybrid fiber. Adsorption kinetic and isotherm tests revealed that Pb2+ and Cd2+ adsorption to the hybrid fiber follows pseudo-second-order kinetic and Langmuir-type adsorption, respectively.
Hajarolasvadi, Setare; Elbanna, Ahmed E.
2017-11-01
The finite difference (FD) and the spectral boundary integral (SBI) methods have been used extensively to model spontaneously-propagating shear cracks in a variety of engineering and geophysical applications. In this paper, we propose a new modelling approach in which these two methods are combined through consistent exchange of boundary tractions and displacements. Benefiting from the flexibility of FD and the efficiency of SBI methods, the proposed hybrid scheme will solve a wide range of problems in a computationally efficient way. We demonstrate the validity of the approach using two examples for dynamic rupture propagation: one in the presence of a low-velocity layer and the other in which off-fault plasticity is permitted. We discuss possible potential uses of the hybrid scheme in earthquake cycle simulations as well as an exact absorbing boundary condition.
DEFF Research Database (Denmark)
Celia, Michael A.; Binning, Philip John
1992-01-01
A numerical algorithm for simulation of two-phase flow in porous media is presented. The algorithm is based on a modified Picard linearization of the governing equations of flow, coupled with a lumped finite element approximation in space and dynamic time step control. Numerical results indicate...... that the algorithm produces solutions that are essentially mass conservative and oscillation free, even in the presence of steep infiltrating fronts. When the algorithm is applied to the case of air and water flow in unsaturated soils, numerical results confirm the conditions under which Richards's equation is valid...... that describe two-phase flow in porous media....
Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics
Kakhktsyan, V. M.; Khachatryan, A. Kh.
2013-07-01
A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.
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Sreetama Banerjee
2017-07-01
Full Text Available We report light-induced negative organic magnetoresistance (OMAR measured in ambient atmosphere in solution-processed 6,13-bis(triisopropylsilylethynylpentacene (TIPS-pentacene planar hybrid devices with two different device architectures. Hybrid electronic devices with trench-isolated electrodes (HED-TIE having a channel length of ca. 100 nm fabricated in this work and, for comparison, commercially available pre-structured organic field-effect transistor (OFET substrates with a channel length of 20 µm were used. The magnitude of the photocurrent as well as the magnetoresistance was found to be higher for the HED-TIE devices because of the much smaller channel length of these devices compared to the OFETs. We attribute the observed light-induced negative magnetoresistance in TIPS-pentacene to the presence of electron–hole pairs under illumination as the magnetoresistive effect scales with the photocurrent. The magnetoresistance effect was found to diminish over time under ambient conditions compared to a freshly prepared sample. We propose that the much faster degradation of the magnetoresistance effect as compared to the photocurrent was due to the incorporation of water molecules in the TIPS-pentacene film.
Xie, Hui; Song, Kang; He, Yu
2014-07-01
A novel solution for electro-hydraulic variable valve timing (VVT) system of gasoline engines is proposed, based on the concept of active disturbance rejection control (ADRC). Disturbances, such as oil pressure and engine speed variations, are all estimated and mitigated in real-time. A feed-forward controller was added to enhance the performance of the system based on a simple and static first principle model, forming a hybrid disturbance rejection control (HDRC) strategy. HDRC was validated by experimentation and compared with an existing manually tuned proportional-integral (PI) controller. The results show that HDRC provided a faster response and better tolerance of engine speed and oil pressure variations. © 2013 ISA Published by ISA All rights reserved.
Zhou, Renjia; Stalder, Romain; Xie, Dongping; Cao, Weiran; Zheng, Ying; Yang, Yixing; Plaisant, Marc; Holloway, Paul H; Schanze, Kirk S; Reynolds, John R; Xue, Jiangeng
2013-06-25
Advances in colloidal inorganic nanocrystal synthesis and processing have led to the demonstration of organic-inorganic hybrid photovoltaic (PV) cells using low-cost solution processes from blends of conjugated polymer and colloidal nanocrystals. However, the performance of such hybrid PV cells has been limited due to the lack of control at the complex interfaces between the organic and inorganic hybrid active materials. Here we show that the efficiency of hybrid PV devices can be significantly enhanced by engineering the polymer-nanocrystal interface with proper chemical treatment. Using two different conjugated polymers, poly(3-hexylthiophene) (P3HT) and poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b']-dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT), we show that treating the polymer:nanocrystal hybrid film in an ethanedithiol-containing acetonitrile solution can increase the efficiency of the hybrid PV devices by 30-90%, and a maximum power conversion efficiency of 5.2 ± 0.3% was obtained in the PCPDTBT:CdSe devices at 0.2 sun (AM 1.5G), which was slightly reduced to 4.7 ± 0.3% at 1 sun. The ethanedithiol treatment did not result in significant changes in the morphology and UV-vis optical absorption of the hybrid thin films; however, infrared absorption, NMR, and X-ray photoelectron spectroscopies revealed the effective removal of organic ligands, especially the charged phosphonic acid ligands, from the CdSe nanorod surface after the treatment, accompanied by the possible monolayer passivation of nanorod surfaces with Cd-thiolates. We attribute the hybrid PV cell efficiency increase upon the ethanedithiol treatment to the reduction in charge and exciton recombination sites on the nanocrystal surface and the simultaneous increase in electron transport through the hybrid film.
Qiu, Shanwen
2012-07-01
In this article, we propose a new grid-free and exact solution method for computing solutions associated with an hybrid traffic flow model based on the Lighthill- Whitham-Richards (LWR) partial differential equation. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a fixed acceleration otherwise. We first present a grid-free solution method for the LWR equation based on the minimization of component functions. We then show that this solution method can be extended to compute the solutions to the hybrid model by proper modification of the component functions, for any concave fundamental diagram. We derive these functions analytically for the specific case of a triangular fundamental diagram. We also show that the proposed computational method can handle fixed or moving bottlenecks.
Method of independent timesteps in the numerical solution of initial value problems
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Porter, A.P.
1976-07-21
In the numerical solution of initial-value problems in several independent variables, the timestep is controlled, especially in the presence of shocks, by a small portion of the logical mesh, what one may call the crisis zone. One is frustrated by the necessity of doing in the whole mesh frequent calculations required by only a small part of the mesh. It is shown that it is possible to choose different timesteps natural to different parts of the mesh and to advance each zone in time only as often as is appropriate to that zone's own natural timestep. Prior work is reviewed and for the first time an investigation of the conditions for well-posedness, consistency and stability in independent timesteps is presented; a new method results. The prochronic and parachronic Cauchy surfaces are identified; and the reasons (well-posedness) for constraining the Cauchy surfaces to be prochronic (as distinct from the method of Grandey), that is, to lie prior to the time of the crisis zone (the zone of least timestep), are indicated. Stability (in the maximum norm) of parabolic equations and (in the L2 norm) of hyperbolic equations is reviewed, without restricting the treatment to linear equations or constant coefficients, and stability of the new method is proven in this framework. The details of the method of independent timesteps, the rules for choosing timesteps and for deciding when to update and when to skip zones, and the method of joining adjacent regions of differing timestep are described. The stability of independent timestep difference schemes is analyzed and exhibited. The economic advantages of the method, which often amount to an order-of-magnitude decrease in running time relative to conventional or implicit difference methods, are noted.
Kaiser, Franz-Joachim; Bassler, Niels; Tölli, Heikki; Jäkel, Oliver
2012-03-01
Modern particle therapy facilities enable sub-millimeter precision in dose deposition. Here, also ionization chambers (ICs) are used, which requires knowledge of the recombination effects. Up to now, recombination is corrected using phenomenological approaches for practical reasons. In this study the effect of the underlying dose distribution on columnar recombination, a quantitative model for initial recombination, is investigated. Jaffé's theory, formulated in 1913 quantifies initial recombination by elemental processes, providing an analytical (closed) solution. Here, we investigate the effect of the underlying charged carrier distribution around a carbon ion track. The fundamental partial differential equation, formulated by Jaffé, is solved numerically taking into account more realistic charge carrier distributions by the use of a computer program (Gascoigne 3D). The investigated charge carrier distributions are based on track structure models, which follow a 1/r(2) behavior at larger radii and show a constant value at small radii. The results of the calculations are compared to the initial formulation and to data obtained in experiments using carbon ion beams. The comparison between the experimental data and the calculations shows that the initial approach made by Jaffé is able to reproduce the effects of initial recombination. The amorphous track structure based charge carrier distribution does not reproduce the experimental data well. A small additional correction in the assessment of the saturation current or charge is suggested by the data. The established model of columnar recombination reproduces the experimental data well, whereas the extensions using track structure models do not show such an agreement. Additionally, the effect of initial recombination on the saturation curve (i.e. Jaffé plot) does not follow a linear behavior as suggested by current dosimetry protocols, therefore higher order corrections (such as the investigated ones) might be
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Buscaglia, G.C.; Lopez, A. [Centro Atomico Bariloche and Inst. Balseiro, Bariloche (Argentina); Bolech, C. [Rutgers - the State Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy
2000-07-01
A numerical method for the solution of the time-dependent Ginzburg-Landau equations is detailed. The method is based on the popular technique of gauge invariant variables. Extension of the method to multiply connected domains is addressed. An implementation of the method is made available through the Web. (orig.)
El-Tom, M E A
1974-01-01
A procedure, using spine functions of degree m, deficiency k-1, for obtaining approximate solutions to nonlinear Volterra integral equations of the second kind is presented. The paper is an investigation of the numerical stability of the procedure for various values of m and k. (5 refs).
Lian, Chenzhou
intervention. The initial transient leading to stationary conditions in unsteady combustion simulations is investigated by considering flow establishment in model combustors. The duration of the transient is shown to be dependent on the characteristic turn-over time for recirculation zones and the time for the chamber pressure to reach steady conditions. Representative comparisons of the time-averaged, stationary results with experiment are presented to document the computations. The flow dynamics and combustion for two sizes of chamber diameters and two different wall thermal boundary conditions are investigated to assess the role of the recirculation regions on the mixing/combustion process in rocket engine combustors. Results are presented in terms of both instantaneous and time-averaged solutions. As a precursor to liquid oxygen/gaseous hydrogen (LO2/GH 2) combustion simulations, the evolution of a liquid nitrogen (LN 2) jet initially at a subcritical temperature and injected into a supercritical environment is first investigated and the results are validated against experimental data. Unsteady simulations of non-reacting LO2/GH 2 are then performed for a single element shear coaxial injector. These cold flow calculations are then extended to reacting LO2/GH 2 flows to demonstrate the capability of the numerical procedure for high-density-gradient supercritical reacting flows.
Numerical Research on Hybrid Fuel Locking Device for Upward Flow Core-Research Reactor
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Huh, Hyung; Cho, Yeong-Garp; Yoo, Yeon-Sik; Ryu, Jeong-Soo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-10-15
The assembly must be held firmly against these forces, but cannot be permanently attached to the support stand because periodic refueling of the reactor requires removal or relocation of each assembly. There are so many kinds of fuel locking device, but they are operated manually. As a part of a new project, we have investigated a hybrid fuel locking device (HFLD) for research reactor which is operated automatically. Prior method of holding down the fuel assembly includes a hybrid zero electromagnet consisting of an electromagnet and a permanent magnet. The role of an electromagnet is converged to zero power for overcoming the lifting power of a permanent magnet by controlling the coil current. At this time, a HFLD is an unlocking state. On the contrary, it is locking state that only a permanent magnet works when the power of an electromagnet is off. The results of a FEM in this work lead to the following conclusions: (1) It is possible that an electromagnet is converged to zero power for overcoming the lifting power of a permanent magnet by remote controlling the coil current. (2) At this time, it is able to detect remotely using proximity sensor whether a HFLD is latched or not.
DEFF Research Database (Denmark)
Barrera Figueroa, Salvador; Jacobsen, Finn; Rasmussen, Knud
2008-01-01
Typically, numerical calculations of the pressure, free-field and random-incidence response of a condenser microphone are carried out on the basis of an assumed displacement distribution of the diaphragm of the microphone; the conventional assumption is that the displacement follows a Bessel func...
Adaptive numerical solutions of the Euler equations in 3D using finite elements
Peraire, J.; Peiro, J.; Formaggia, L.; Morgan, K.
1989-01-01
The development of an adaptive mesh solution for a flow involving shock interaction on a swept cylinder and an initial solution for a flow past a complex fighter configuration is reported. The finite element solution algorithm, the mesh generation, and the adaptivity of the solution are described. Sample results for the flow past an F-18 configuration at Mach 0.9 and alpha of 3 deg and for shock interaction on a swept cylinder at Mach 8.04 are summarized.
NUMERICAL AND ANALYTIC SOLUTION OF PRANDTL’S EQUATION FOR SOLID BODIES WITH AGREED CONTACT SURFACES
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A. Chigarev
2013-01-01
Full Text Available The paper considers a method for problem solution pertaining to compression of elastic bodies bounded by cylindrical surfaces whose radii are almost equal. The objective aim does not allow to apply the Hertz theory and reduces to finding approximate solutions of the Prandtl’s equation. The resulting solution is compared with the solution in the ANSYS system.
Numerical solution of newton´s cooling differential equation by the methods of euler and runge-kutta
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Andresa Pescador
2016-04-01
Full Text Available This article presents the first-order differential equations, which are a very important branch of mathematics as they have a wide applicability, in mathematics, as in physics, biology and economy. The objective of this study was to analyze the resolution of the equation that defines the cooling Newton's law. Verify its behavior using some applications that can be used in the classroom as an auxiliary instrument to the teacher in addressing these contents bringing answers to the questions of the students and motivating them to build their knowledge. It attempted to its resolution through two numerical methods, Euler method and Runge -Kutta method. Finally, there was a comparison of the approach of the solution given by the numerical solution with the analytical resolution whose solution is accurate.
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Jyoti Talwar
2012-01-01
Full Text Available In this piece of work using only three grid points, we propose two sets of numerical methods in a coupled manner for the solution of fourth-order ordinary differential equation uiv(x=f(x,u(x,u′(x,u′′(x,u′′′(x, a
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Panou G.
2017-02-01
Full Text Available The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.
Vorsanova, S G; Kolotiĭ, A D; Iurov, I Iu; Kirillova, E A; Monakhov, V V; Beresheva, A K; Solov'ev, I V; Iurov, Iu B
2005-11-01
According to different estimates, as high as 15-20% of all the pregnancies result in spontaneous abortions (SA) at different gestational periods. Identification of abnormalities leading to SA is of great importance for practical medicine, mainly for medical genetic counseling of married couples with impaired reproductive function. The diagnosis of chromosomal aberrations on the basis of SA materials is known to have a number of methodological difficulties. The present paper deals with the identification of numerical anomalies in the SA material by multicolor fluorescence in situ hybridization (MFISH). This technique using an original collection of DNA probes for chromosomes 1, 9, 13/21, 14/22, 15, 16, 18, X, and Y was applied to the study of chromosomal aberrations in 224 spontaneous abortion specimens. Numerical chromosomal aberrations were found in 122 (54.5%) cases. The cells of all the studied specimens exhibited aneuploidy of chromosome X in 17% cases; chromosome 16 in 12%, chromosomes 13/21 in 5.8%, chromosomes 14/22 in 4.9%, chromosomes 9 and 18 in 1.3% (each), chromosome 15 in 0.9%, chromosome 1 in 0.45%. Polyploidy was detected in 13.3% of cases; concomitant abnormalities were found in 7 cases. Analysis of the findings has led to the conclusion that MFISH can be successfully used in the diagnosis of numerical chromosomal aberrations of CA cells.
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Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
Saha Ray, S.
2013-12-01
In this paper, the modified fractional reduced differential transform method (MFRDTM) has been proposed and it is implemented for solving fractional KdV (Korteweg-de Vries) equations. The fractional derivatives are described in the Caputo sense. In this paper, the reduced differential transform method is modified to be easily employed to solve wide kinds of nonlinear fractional differential equations. In this new approach, the nonlinear term is replaced by its Adomian polynomials. Thus the nonlinear initial-value problem can be easily solved with less computational effort. In order to show the power and effectiveness of the present modified method and to illustrate the pertinent features of the solutions, several fractional KdV equations with different types of nonlinearities are considered. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of fractional KdV equations.
1993-04-01
et al. Finite Elements An Introduction. Volume I. Englewood Cliffs, New Jersey: Prentice-Hall, 1981. Chapra , Steven C. and Canale, Raymond P. Numerical...1981. 2. Chapra , Steven C. and Canale, Raymond P. Numerical Methods For Engineers. New York: McGraw-Hill Book Company, 1985 3. Chandrupatla, Tirupathi
Numerical solution of nonlinear acoustic wave problems employing a green's function approach
Huijssen, J.; Verweij, M.D.
2006-01-01
The design of phased array transducers for medical diagnostic ultrasound asks for an understanding of the nonlinear propagation of acoustic wavefields. Most existing numerical models are based on the linearized model equations, but in the recent decades several numerical models have been developed
Numerical solution of nonlinear Volterra-Fredholm integral equation by using Chebyshev polynomials
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R. Ezzati
2011-03-01
Full Text Available In this paper, we have used Chebyshev polynomials to solve linearand nonlinear Volterra-Fredholm integral equations, numerically.First we introduce these polynomials, then we use them to changethe Volterra-Fredholm integral equation to a linear or nonlinearsystem. Finally, the numerical examples illustrate the efficiencyof this method.
Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.
2017-09-01
Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.
Munteanu, Mihaela; Dascălu, Gabriela
2012-01-01
Widely use of reinforced concrete frame structures highlights the elements study of this structure type. Analysis of reinforced concrete slabs is supported by technical and economic objectives that aim to obtain innovative and feasible solutions. In this respect, the solution of hollow voided slabs is analysed in comparison with classic slab floor, stating the advantages and disadvantages of these two solutions. Previous testing and study of these variant represent another factor to be achiev...
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Emran Tohidi
2016-01-01
Full Text Available This article contributes a matrix approach by using Taylor approximation to obtain the numerical solution of one-dimensional time-dependent parabolic partial differential equations (PDEs subject to nonlocal boundary integral conditions. We first impose the initial and boundary conditions to the main problems and then reach to the associated integro-PDEs. By using operational matrices and also the completeness of the monomials basis, the obtained integro-PDEs will be reduced to the generalized Sylvester equations. For solving these algebraic systems, we apply a famous technique in Krylov subspace iterative methods. A numerical example is considered to show the efficiency of the proposed idea.
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Teixeira, Vinicius Ligiero; Pires, Adolfo Puime; Bedrikovetsky, Pavel G. [Universidade Estadual do Norte Fluminense (UENF), Macae, RJ (Brazil). Lab. de Engenharia e Exploracao do Petroleo (LENEP)
2004-07-01
Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. The EOR methods may be classified into the following kinds: injection of chemical solutions, injection of solvents and thermal methods. The chemical fluids most commonly injected are polymers, surfactants, micellar solutions, etc. Displacement of oil by any of these fluids involves complex physico-chemical processes of interphase mass transfer, phase transitions and transport properties changes. These processes can be divided into two main categories: thermodynamical and hydrodynamical ones. They occur simultaneously during the displacement, and are coupled in the modern mathematical models of EOR. The model for one-dimensional displacement of oil by polymer solutions is analyzed in this paper. The Courant number is fixed, and we compare the results of different runs of a numerical simulator with the analytical solution of this problem. Each run corresponds to a different spatial discretization. (author)
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M. I. Berenguer
2009-01-01
Full Text Available In this work we use analytical tools—Schauder bases and Geometric Series theorem—in order to develop a new method for the numerical resolution of the linear Volterra integral equation of the second kind.
Denisov, A. M.; Zakharov, E. V.; Kalinin, A. V.; Kalinin, V. V.
2010-07-01
A numerical method is proposed for solving an inverse electrocardiography problem for a medium with a piecewise constant electrical conductivity. The method is based on the method of boundary integral equations and Tikhonov regularization.
On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations
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H. Montazeri
2012-01-01
Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.
Numerical solution of neutral functional-differential equations with proportional delays
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Mehmet Giyas Sakar
2017-07-01
Full Text Available In this paper, homotopy analysis method is improved with optimal determination of auxiliary parameter by use of residual error function for solving neutral functional-differential equations (NFDEs with proportional delays. Convergence analysis and error estimate of method are given. Some numerical examples are solved and comparisons are made with the existing results. The numerical results show that the homotopy analysis method with residual error function is very effective and simple.
Hilbert space method for the numerical solution of reactor physics problems
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Ackroyd, R.T. (UKAEA Risley Nuclear Power Development Labs.)
1983-01-01
A Hilbert space approach is used to give a unified treatment of neutron transport by finite element methods. Global solutions can be found by least squares, variational and weighted residual methods stemming from an identity. Bounds for local characteristics of solutions are found by a bi-variational method.
Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
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Khaled A. Gepreel
2013-01-01
Full Text Available We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved -expansion function method to find exact solutions of nonlinear fractional BBM equation.
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Susmita Paul
2016-03-01
Full Text Available This paper reflects some research outcome denoting as to how Lotka–Volterra prey predator model has been solved by using the Runge–Kutta–Fehlberg method (RKF. A comparison between Runge–Kutta–Fehlberg method (RKF and the Laplace Adomian Decomposition method (LADM is carried out and exact solution is found out to verify the applicability, efficiency and accuracy of the method. The obtained approximate solution shows that the Runge–Kutta–Fehlberg method (RKF is a more powerful numerical technique for solving a system of nonlinear differential equations.
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Mehriban Imanova Natiq
2012-03-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE As is known, many problems of natural science are reduced mainly to the solution of nonlinear Volterra integral equations. The method of quadratures that was first applied by Volterra to solving variable boundary integral equations is popular among numerical methods for the solution of such equations. At present, there are different modifications of the method of quadratures that have bounded accuracies. Here we suggest a second derivative multistep method for constructing more exact methods.
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Fukang Yin
2013-01-01
Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.
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Balci, Mustafa H. [Department of Materials Science and Engineering, NTNU, 7491 Trondheim (Norway); Aas, Lars Martin Sandvik; Kildemo, Morten; Sæterli, Ragnhild; Holmestad, Randi; Lindgren, Mikael [Department of Physics, NTNU, 7491 Trondheim (Norway); Grande, Tor [Department of Materials Science and Engineering, NTNU, 7491 Trondheim (Norway); Einarsrud, Mari-Ann, E-mail: Mari-Ann.Einarsrud@ntnu.no [Department of Materials Science and Engineering, NTNU, 7491 Trondheim (Norway)
2016-03-31
Silicon nano-crystals have been studied intensively due to their photoluminescence properties and possible applications in new generation opto-electronic devices. Their importance in lightning and display technologies is increasing due to the abundance and non-toxicity of silicon. Here we report a single batch solution based synthesis route to silicon nano-crystal organic hybrid films exhibiting white light photoluminescence at room temperature upon excitation by ultraviolet light. Films prepared by ethylene glycol terminated Si nano-crystals showed maximum 240 nm red shift in photoluminescence response upon excitation at 350 nm. The shift was found to decrease in order for hybrid films fabricated using acrylic acid, 1-octanol acid and oleic acid terminated Si nano-crystals. The mean size of the Si nano-crystals (~ 2–10 nm) estimated by Raman spectroscopy were smallest for the ethylene glycol capped Si nano-crystal films. The calculated Tauc bandgaps of the hybrid films varied between 1.51 and 2.35 eV. - Highlights: • White light emitting Si nanocrystal hybrid films were synthesized at low temperature • The effect of the surface termination of the Si nano-crystals is reported • A red shift in photoluminescence response was observed • The hybrid films are new candidate white light emitting diodes • The hybrid films can be used in solar cell applications for spectral-shifting control.
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A. H. Bhrawy
2012-01-01
Full Text Available A shifted Jacobi Galerkin method is introduced to get a direct solution technique for solving the third- and fifth-order differential equations with constant coefficients subject to initial conditions. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. A quadrature Galerkin method is introduced for the numerical solution of these problems with variable coefficients. A new shifted Jacobi collocation method based on basis functions satisfying the initial conditions is presented for solving nonlinear initial value problems. Through several numerical examples, we evaluate the accuracy and performance of the proposed algorithms. The algorithms are easy to implement and yield very accurate results.
Yon, Steven; Katz, Joseph; Plotkin, Allen
1992-01-01
The practical limit of airfoil thickness ratio for which acceptable engineering results are obtainable with the Dirichlet boundary-condition-based numerical methods is investigated. This is done by studying the effect of thickness on the calculated pressure distribution near the trailing edge and by comparing the aerodynamic coefficients with available exact solutions. The first objective of this study, owing to the wide use of such computational methods, is to demonstrate the numerical symptoms that occur when the body or wing thickness approaches zero and to increase the awareness of potential users of these methods. Additionally, an effort is made to obtain the practical limits of the trailing-edge thickness where such problems will appear in the flow solution, and to propose some possible cures for very thin airfoils or those with cusped trailing edges.
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Ackroyd, R.T.; Oliveira, C.R.E. de [Imperial Coll. of Science, Technology and Medicine, London (United Kingdom). Dept. of Mechanical Engineering
1996-09-01
A maximum principle for the time-dependent first-order Boltzmann equation is established in two independent ways:- by a generalized least squares method and by a method based on the properties of an appropriate bi-linear form. The second derivation suggests a metric for a Hilbert space which provides a geometrical interpretation of the variational principle. This interpretation leads to a Petrov-Galerkin method of Martin for time dependent transport. The maximum principle is used to define a figure of merit for the global error of any numerical solution for time dependent transport. The principle is used also to demonstrate the neutron conservation property of optimized numerical solutions, and the convergence of finite element methods based on the variational principle. (Author).
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M. Zellerhoff
2003-01-01
Full Text Available Due to the increasing importance of EMC problems through the last years there is a great interest in measurement devices such as GTEM-cells (Giga(Hz- TEM cells. They promise to allow compact and low-cost emission- as well as susceptibility tests up to very high frequencies. Expensive measurement procedures in open-area test sites or within semi-anechoic chambers would become obsolete in many cases. To estimate the quality and reliability of GTEM-cell measurements it is necessary to have detailed knowledge about the processes within the cell and, in particular, about the interactions between the cell and the DUT (device under test. Due to the high frequency and the cell’s dimensions a purely numerical simulation while using standard techniques such as Finite Element Method, Method of Moments (MoM or the Finite-Differ-Time-Domain (FDTD method is inefficient and unnecessary since the GTEM-cell is a mostly empty homogeneous TEM-waveguide. Analytical models allow only the investigation of empty cells. As will be outlined in the following, a suitable way to reduce the numerical complexity of the general problem is the use of a hybrid method, such as the combination of a modal analysis with the MoM.
Tsujii, N.; Takase, Y.; Ejiri, A.; Shinya, T.; Togashi, H.; Yajima, S.; Yamazaki, H.; Moeller, C. P.; Roidl, B.; Sonehara, M.; Takahashi, W.; Toida, K.; Yoshida, Y.
2017-12-01
Non-inductive plasma start-up is a critical issue for spherical tokamaks since there is not enough room to provide neutron shielding for the center solenoid. Start-up using lower hybrid (LH) waves has been studied on the TST-2 spherical tokamak. Because of the low magnetic field of a spherical tokamak, the plasma density needs to be kept at a very low value during the plasma current ramp-up so that the plasma core remains accessible to the LH waves. However, we have found that higher density was required to sustain larger plasma current. The achievable plasma current was limited by the maximum operational toroidal field of TST-2. The existence of an optimum density for LH current drive and its toroidal field dependence is explained through a numerical simulation based on a ray tracing code and a Fokker-Planck solver. In order to access higher density at the same magnetic field, a top-launch antenna was recently installed in addition to the existing outboard-launch antenna. Increase in the density limit was observed when the power was launched from the top antenna, consistently with the numerical predictions.
Balla, Hyder H; Abdullah, Shahrir; Mohdfaizal, Wan; Zulkifli, Rozli; Sopian, Kamaruzaman
2013-01-01
A numerical simulation model for laminar flow of nanofluids in a pipe with constant heat flux on the wall was built to study the effect of the Reynolds number on convective heat transfer and pressure loss. The investigation was performed for hybrid nanofluids consisting of CuO-Cu nanoparticles and compared with CuO and Cu in which the nanoparticles have a spherical shape with size 50, 50, 50nm respectively. The nanofluids were prepared, following which the thermal conductivity and dynamic viscosity were measured for a range of temperatures (10 -60°C). The numerical results obtained were compared with the existing well-established correlation. The prediction of the Nusselt number for nanofluids agrees well with the Shah correlation. The comparison of heat transfer coefficients for CuO, Cu and CuO-Cu presented an increase in thermal conductivity of the nanofluid as the convective heat transfer coefficient increased. It was found that the pressure loss increases with an increase in the Reynolds number, nanoparticle density and particle volume fraction. However, the flow demonstrates enhancement in heat transfer which becomes greater with an increase in the Reynolds number for the nanofluid flow.
Numerical analysis of using hybrid photovoltaic-thermal solar water heater in Iran
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M Mohammadi Sarduei
2017-05-01
Full Text Available Introduction Electrical performance of solar cells decreases with increasing cell temperature, basically because of growth of the internal charge carrier recombination rates, caused by increased carrier concentrations. Hybrid Photovoltaic/thermal (PVT systems produce electrical and thermal energy simultaneously. PVT solar collectors convert the heat generated in the solar cells to low temperature useful heat energy and so they provide a lower working temperature for solar cells which subsequently leads to a higher electrical efficiency. Recently, in Iran, the reforming government policy in subsidy and increasing fossil fuels price led to growing an interest in use of renewable energies for residual and industrial applications. In spite of this, the PV power generator investment is not economically feasible, so far. Hybrid PVT devices are well known as an alternative method to improve energy performance and therefore economic feasibility of the conventional PV systems. The aim of this study is to investigate the performance of a PVT solar water heater in four different cities of Iran using TRNSYS program. Materials and Methods The designed PVT solar water system consists of two separate water flow circuits namely closed cycle and open circuit. The closed cycle circuit was comprised of a solar PVT collector (with nominal power of 880 W and area of 5.6 m2, a heat exchanger in the tank (with volume of 300 L, a pump and connecting pipes. The water stream in the collector absorbs the heat accumulated in the solar cells and delivers it to the water in the tank though the heat exchanger. An on/off controller system was used to activate the pump when the collector outlet temperature was higher than that of the tank in the closed cycle circuit. The water in the open circuit, comes from city water at low temperature, enters in the lower part of the storage tank where the heat transfer occurs between the two separate circuits. An auxiliary heater, connected
Directory of Open Access Journals (Sweden)
Vincenzo Maria De Benedictis
2016-05-01
Full Text Available The Mark–Houwink–Sakurada (MHS equation allows for estimation of rheological properties, if the molecular weight is known along with good understanding of the polymer conformation. The intrinsic viscosity of a polymer solution is related to the polymer molecular weight according to the MHS equation, where the value of the constants is related to the specific solvent and its concentration. However, MHS constants do not account for other characteristics of the polymeric solutions, i.e., Deacetilation Degree (DD when the solute is chitosan. In this paper, the degradation of chitosan in different acidic environments by thermal treatment is addressed. In particular, two different solutions are investigated (used as solvent acetic or hydrochloric acid with different concentrations used for the preparation of chitosan solutions. The samples were treated at different temperatures (4, 30, and 80 °C and time points (3, 6 and 24 h. Rheological, Gel Permeation Chromatography (GPC, Fourier Transform Infrared Spectroscopy (FT-IR, Differential Scanning Calorimetry (DSC and Thermal Gravimetric Analyses (TGA were performed in order to assess the degradation rate of the polymer backbones. Measured values of molecular weight have been integrated in the simulation of the batch degradation of chitosan solutions for evaluating MHS coefficients to be compared with their corresponding experimental values. Evaluating the relationship between the different parameters used in the preparation of chitosan solutions (e.g., temperature, time, acid type and concentration, and their contribution to the degradation of chitosan backbone, it is important to have a mathematical frame that could account for phenomena involved in polymer degradation that go beyond the solvent-solute combination. Therefore, the goal of the present work is to propose an integration of MHS coefficients for chitosan solutions that contemplate a deacetylation degree for chitosan systems or a more
Directory of Open Access Journals (Sweden)
Z. Mosayebi
2014-07-01
Full Text Available In this paper a numerical technique is presented for the solution of fuzzy linear Volterra-Fredholm-Hammerstein integral equations. This method is a combination of collocation method and radial basis functions(RBFs.We first solve the actual set are equivalent to the fuzzy set, then answer 1-cut into the equation. Also high convergence rates and good accuracy are obtain with the propose method using relativeiy low numbers of data points.
Dryazhenkov, A. A.; Potapov, M. M.
2016-02-01
An algorithm for solving a quadratic minimization problem on an ellipsoidal set in a Hilbert space is proposed. The algorithm is stable to nonuniform perturbations of the operators. A key condition for its application is that we know an estimate for the norm of the exact solution. Applications to boundary control problems for the one-dimensional wave equation are considered. Numerical results are presented.
Adsorption of azo dyes from aqueous solution by the hybrid MOFs/GO.
Li, Ling; Shi, Zhennan; Zhu, Hongyang; Hong, Wei; Xie, Fengwei; Sun, Keke
2016-01-01
In this work, a hybrid of chromium(III) terephthalate metal organic framework (MIL-101) and graphene oxide (GO) was synthesized and its performance in the removal of azo dyes (Amaranth, Sunset Yellow, and Carmine) from water was evaluated. The adsorption for azo dyes on MIL-101/GO was compared with that of MIL-101, and it was found that the addition of GO enhanced the stability of MIL-101 in water and increased the adsorption capacity. The maximum adsorption capacities of MIL-101/GO were 111.01 mg g(-1) for Amaranth, 81.28 mg g(-1) for Sunset Yellow, and 77.61 mg g(-1) for Carmine. The adsorption isotherms and kinetics were investigated, showing that the adsorption fits the Freundlich isotherm and the pseudo-second-order kinetic model. The recyclability of MIL-101/GO was shown by the regeneration by acetone. The high adsorption capability and excellent reusability make MIL-101/GO a competent adsorbent for the removal dyes from aqueous solution.
An All-Solution-Based Hybrid CMOS-Like Quantum Dot/Carbon Nanotube Inverter.
Shulga, Artem G; Derenskyi, Vladimir; Salazar-Rios, Jorge Mario; Dirin, Dmitry N; Fritsch, Martin; Kovalenko, Maksym V; Scherf, Ullrich; Loi, Maria A
2017-09-01
The development of low-cost, flexible electronic devices is subordinated to the advancement in solution-based and low-temperature-processable semiconducting materials, such as colloidal quantum dots (QDs) and single-walled carbon nanotubes (SWCNTs). Here, excellent compatibility of QDs and SWCNTs as a complementary pair of semiconducting materials for fabrication of high-performance complementary metal-oxide-semiconductor (CMOS)-like inverters is demonstrated. The n-type field effect transistors (FETs) based on I(-) capped PbS QDs (Vth = 0.2 V, on/off = 10(5) , SS-th = 114 mV dec(-1) , µe = 0.22 cm(2) V(-1) s(-1) ) and the p-type FETs with tailored parameters based on low-density random network of SWCNTs (Vth = -0.2 V, on/off > 10(5) , SS-th = 63 mV dec(-1) , µh = 0.04 cm(2) V(-1) s(-1) ) are integrated on the same substrate in order to obtain high-performance hybrid inverters. The inverters operate in the sub-1 V range (0.9 V) and have high gain (76 V/V), large maximum-equal-criteria noise margins (80%), and peak power consumption of 3 nW, in combination with low hysteresis (10 mV). © 2017 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Hoseinian, Fatemeh Sadat; Rezai, Bahram; Kowsari, Elaheh
2017-12-15
Prediction of Ni(II) removal during ion flotation is necessary for increasing the process efficiency by suitable modeling and simulation. In this regard, a new predictive model based on the hybrid neural genetic algorithm (GANN) was developed to predict the Ni(II) ion removal and water removal during the process from aqueous solutions using ion flotation. A multi-layer GANN model was trained to develop a predictive model based on the important effective variables on the Ni(II) ion flotation. The input variables of the model were pH, collector concentration, frother concentration, impeller speed and flotation time, while the removal percentage of Ni(II) ions and water during ion flotation were the outputs. The most effective input variables on Ni(II) removal and water removal were evaluated using the sensitivity analysis. The sensitivity analysis of the model shows that all input variables have a significant impact on the outputs. The results show that the proposed GANN models can be used to predict the Ni(II) removal and water removal during ion flotation. Copyright © 2017 Elsevier Ltd. All rights reserved.
Dlugach, Janna M.; Mishchenko, Michael I.
2017-01-01
In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.
Goloviznin, V. M.; Kanaev, A. A.
2012-03-01
The CABARET computational algorithm is generalized to one-dimensional scalar quasilinear hyperbolic partial differential equations with allowance for inequality constraints on the solution. This generalization can be used to analyze seepage of liquid radioactive wastes through the unsaturated zone.
Tin melting: Effect of grid size and scheme on the numerical solution
Directory of Open Access Journals (Sweden)
Vasilios Alexiades
2003-02-01
Full Text Available Benchmark solutions in Computational Fluid Dynamics are necessary for testing and for the verification of newly developed algorithms and codes. For flows involving heat transfer coupled to solid-liquid phase change and convection in the melt, such benchmark solutions do not exist. A set of benchmark problems has recently been proposed for melting of metals and waxes and several researchers responded by providing solutions for the given problems. It was shown in two recent publications that there were large discrepancies in the results obtained by those contributors. In the present, work we focus on one of the four test problems, tin melting at Rayleigh number $Ra=2.5imes 10^{5}$. Solutions obtained for several grids and two discretization schemes are presented and compared. Our results are used to explain the origin of the discrepancies in earlier results. Suggestions for future work are also provided.
Solution of AntiSeepage for Mengxi River Based on Numerical Simulation of Unsaturated Seepage
Directory of Open Access Journals (Sweden)
Youjun Ji
2014-01-01
Full Text Available Lessening the leakage of surface water can reduce the waste of water resources and ground water pollution. To solve the problem that Mengxi River could not store water enduringly, geology investigation, theoretical analysis, experiment research, and numerical simulation analysis were carried out. Firstly, the seepage mathematical model was established based on unsaturated seepage theory; secondly, the experimental equipment for testing hydraulic conductivity of unsaturated soil was developed to obtain the curve of two-phase flow. The numerical simulation of leakage in natural conditions proves the previous inference and leakage mechanism of river. At last, the seepage control capacities of different impervious materials were compared by numerical simulations. According to the engineering actuality, the impervious material was selected. The impervious measure in this paper has been proved to be effectible by hydrogeological research today.
On the efficient numerical solution of lattice systems with low-order couplings
Energy Technology Data Exchange (ETDEWEB)
Ammon, A. [OAKLABS GmbH, Hennigsdorf (Germany); Genz, A. [Washington State Univ., Pullman, WA (United States). Dept. of Mathematics; Hartung, T. [King' s College London (United Kingdom). Dept. of Mathematics; Jansen, K.; Volmer, J. [DESY Zeuthen (Germany). NIC; Leoevey, H. [Humboldt Univ. Berlin (Germany). Inst. fuer Mathematik
2015-10-15
We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model. For the anharmonic oscillator both methods outperform standard Markov Chain Monte Carlo methods and show a significantly improved error scaling. For the quantum mechanical rotor we could, however, not find a successful way employing QMC. On the other hand, the recursive numerical integration method works extremely well for this model and shows an at least exponentially fast error scaling.
Sweilam, N. H.; Abou Hasan, M. M.
2017-05-01
In this paper, the weighted-average non-standard finite-difference (WANSFD) method is used to study numerically the general time-fractional nonlinear, one-dimensional problem of thermoelasticity. This model contains the standard system arising in thermoelasticity as a special case. The stability of the proposed method is analyzed by a procedure akin to the standard John von Neumann technique. Moreover, the accuracy of the proposed scheme is proved. Numerical results are presented graphically, which reveal that the WANSFD method is easy to implement, effective and convenient for solving the proposed system. The proposed method could also be easily extended to solve other systems of fractional partial differential equations.
Russo, David
2016-05-01
The aim of the present numerical study was to extend the data-driven protocol for the control of soil salinity, to control chloride and nitrate concentrations and mass fluxes below agricultural fields irrigated with treated waste water (TWW). The protocol is based on alternating irrigation water quality between TWW and desalinized water (DSW), guided by solute concentrations at soil depth, zs. Two different schemes, the first requires measurements of soil solution concentrations of chloride and nitrate at zs, while, the second scheme requires only measurements of soil solution EC at zs, were investigated. For this purpose, 3-D numerical simulations of flow and transport were performed for variably saturated, spatially heterogeneous, flow domains located at two different field sites. The sites differ in crop type, irrigation method, and in their lithology; these differences, in turn, considerably affect the performance of the proposed schemes, expressed in terms of their ability to reduce solute concentrations that drained below the root zone. Results of the analyses suggest that the proposed data-driven schemes allow the use of low-quality water for irrigation, while minimizing the consumption of high-quality water to a level, which, for given climate, soil, crop, irrigation method, and water quality, may be determined by the allowable nitrate and chloride concentrations in the groundwater. The results of the present study indicate that with respect to the diminution of groundwater contamination by chloride and nitrate, the more data demanding, first scheme is superior the second scheme.
Goulet, R.; Knikker, R.; Boudard, E.; Stutz, B.; Bonjour, J.
2014-02-01
This paper describes a numerical and experimental analysis of the process of water vapour absorption by a static lithium bromide solution. In the experiment, the temperature evolution of the absorbent solution is measured at different heights. The numerical model solves the set of governing equations for the simultaneous heat and mass transfer inside the absorbent by means of the finite-volume method. An iterative method is used to take into account the strong coupling of heat and mass transfer at the interface and variations of thermophysical properties. A moving grid technique is employed to represent the increase of the solution volume. Model results are compared with our measurements and data reported in the literature. The influence of using constant properties is analysed by comparison with the variable properties and experimental results. It is found that this assumption provides acceptable results in the investigated pool absorption cases despite a strong underestimation of the increase of the solution volume in the course of the absorption process.
Global communication schemes for the numerical solution of high-dimensional PDEs
DEFF Research Database (Denmark)
Hupp, Philipp; Heene, Mario; Jacob, Riko
2016-01-01
The numerical treatment of high-dimensional partial differential equations is among the most compute-hungry problems and in urgent need for current and future high-performance computing (HPC) systems. It is thus also facing the grand challenges of exascale computing such as the requirement to red...
A mathematical model and numerical solution of interface problems for steady state heat conduction
Directory of Open Access Journals (Sweden)
Z. Muradoglu Seyidmamedov
2006-01-01
(isolation Ωδ tends to zero. For each case, the local truncation errors of the used conservative finite difference scheme are estimated on the nonuniform grid. A fast direct solver has been applied for the interface problems with piecewise constant but discontinuous coefficient k=k(x. The presented numerical results illustrate high accuracy and show applicability of the given approach.
Czech Academy of Sciences Publication Activity Database
Pokorný, Vladislav; Žonda, M.; Kauch, Anna; Janiš, Václav
2017-01-01
Roč. 131, č. 4 (2017), s. 1042-1044 ISSN 0587-4246 R&D Projects: GA ČR GA15-14259S Institutional support: RVO:68378271 Keywords : Anderson model * parquet equations * numerical renormalization group Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.469, year: 2016
A three–step discretization scheme for direct numerical solution of ...
African Journals Online (AJOL)
In this paper, a three-step discretization (numerical) formula is developed for direct integration of second-order initial value problems in ordinary differential equations. The development of the method and analysis of its basic properties adopt Taylor series expansion and Dahlquist stability test methods. The results show that ...
Quintic B-spline for the numerical solution of the good Boussinesq equation
Directory of Open Access Journals (Sweden)
Shahid S. Siddiqi
2014-07-01
Full Text Available A numerical method is developed to solve the nonlinear Boussinesq equation using the quintic B-spline collocation method. Applying the Von Neumann stability analysis, the proposed method is shown to be unconditionally stable. An example has been considered to illustrate the efficiency of the method developed.
Numerical solution of the transverse resistivity of superconducting cables under AC conditions
Hartmann, R.A.; Hartmann, R.A.; van Beckum, F.P.H.; van de Klundert, L.J.M.; van de Klundert, L.J.M.; Dijkstra, D.
1989-01-01
The authors develop a numerical method for calculating the transverse resistivity of superconducting cables. A superconducting cable consists of a twisted bundle of strands with a nonconducting inner region. If such a cable is placed in an external magnetic field, the induced currents will not
Directory of Open Access Journals (Sweden)
Jafar Biazar
2015-01-01
Full Text Available We combine the Adomian decomposition method (ADM and Adomian’s asymptotic decomposition method (AADM for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.
DEFF Research Database (Denmark)
Lee, Jonghyun; Rolle, Massimo; Kitanidis, Peter K.
2017-01-01
such parameterization is by far the most commonly used in solute transport applications, its validity has been questioned. Here, our goal is to investigate the effects of heterogeneity and mass transfer limitations on block-scale longitudinal dispersion and to evaluate under which conditions the Scheidegger...... parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection...... meaning of the method and we show how the block longitudinal dispersivity approaches, under certain conditions, the Scheidegger limit at large PÃ©clet numbers. Lastly, we discuss the potential and limitations of the method to accurately describe dispersion in solute transport applications in heterogeneous...
Nonlinear grid error effects on numerical solution of partial differential equations
Dey, S. K.
1980-01-01
Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.
Henle, James M.
This pamphlet consists of 17 brief chapters, each containing a discussion of a numeration system and a set of problems on the use of that system. The numeration systems used include Egyptian fractions, ordinary continued fractions and variants of that method, and systems using positive and negative bases. The book is informal and addressed to…
Monnier, Raoul; Mourelle, Aurora; Bernoux, Jean-Paul; Alberti, Claudio; Le Feuvre, Jean; Hamidouche, Wassim
2015-01-01
Broadcast and broadband networks continue to be separate worlds in the video consumption business. Some initiatives such as HbbTV have built a bridge between both worlds, but its application is almost limited to providing links over the broadcast channel to content providers’ applications such as Catch-up TV services. When it comes to reality, the user is using either one network or the other. H2B2VS is a Celtic-Plus project aiming at exploiting the potential of real hybrid networks by implem...
Numerical solution of Painlev'e equation I by Daftardar-Gejji and Jafari method
Selamat, M. S.; Latif, B.; Aziz, N. A.; Yahya, F.
2017-08-01
In this paper, Painlev'e equation I problem was solved approximately using Daftardar-Gejji and Jafari Method (DJM) with initial conditions. The results obtained through this iterative method, is compared with that obtained by other methods such as Adomian Decomposition Method (ADM), Homotopy Pertubation Method (HPM) and Variational Iteration Method (VIM). The numerical results show that there is no significant difference. It has been found that the results obtained are in fully agreement.
Editorial: Special Issue on Analytical and Approximate Solutions for Numerical Problems
Walailak Journal of Science and Technology
2014-01-01
Though methods and algorithms in numerical analysis are not new, they have become increasingly popular with the development of high speed computing capabilities. Indeed, the ready availability of high speed modern digital computers and easy-to-employ powerful software packages has had a major impact on science, engineering education and practice in the recent past. Researchers in the past had to depend on analytical skills to solve significant engineering problems but, nowadays, researchers h...
Direct numerical solution of Poisson`s equation in cylindrical (r, z) coordinates
Energy Technology Data Exchange (ETDEWEB)
Chao, E.H.; Paul, S.F.; Davidson, R.C. [Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.; Fine, K.S. [Univ. of California, San Diego, La Jolla (Canada). Dept. of Physics
1997-07-22
A direct solver method is developed for solving Poisson`s equation numerically for the electrostatic potential {phi}(r,z) in a cylindrical region (r < R{sub wall}, 0 < z < L). The method assumes the charge density {rho}(r,z) and wall potential {phi}(r = R{sub wall}, z) are specified, and {partial_derivative}{phi}/{partial_derivative}z = 0 at the axial boundaries (z = 0, L).
AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L2 OPTIMAL MASS TRANSFER PROBLEM*
Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen
2010-01-01
In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L2 mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61–97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data. PMID:21278828
On the numerical solution of the Gross–Pitaevskii equation | Laoye ...
African Journals Online (AJOL)
... Bogoliubov–de Gennes equations for type II superconductivity. The solution is compared with others in the literature and is shown to be easily adapted to the study of an isolated vortex recently discovered in Bose-Einstein Condensation in trapped gases. Journal of the Nigerian Association of Mathematical Physics Vol.
A comparison of numerical methods for the solution of continuous-time DSGE models
DEFF Research Database (Denmark)
Parra-Alvarez, Juan Carlos
This paper evaluates the accuracy of a set of techniques that approximate the solution of continuous-time DSGE models. Using the neoclassical growth model I compare linear-quadratic, perturbation and projection methods. All techniques are applied to the HJB equation and the optimality conditions...
Energy Technology Data Exchange (ETDEWEB)
Shamim, Jubair Ahmed; Bhowmik, Palash Kumar; Suh, Kune Y. [Seoul National Univ., Seoul (Korea, Republic of)
2014-05-15
Most of the traditional ways available in the literature to enhance heat transfer are mainly based on variation of structures like addition of heat surface area such as fins, vibration of heated surface, injection or suction of fluids, applying electrical or magnetic fields, and so forth. Application of these mechanical techniques to a fuel rod bundle will involve not only designing complex geometries but also using many additional mechanisms inside a nuclear reactor core which in turn will certainly increase the manufacturing cost as well as may hamper various safety features essential for sound and uninterrupted operation of a nuclear power reactor. On the other hand, traditional heat transfer fluids such as water, ethylene glycol and oils have inherently low thermal conductivity relative to metals and even metal oxides. In this study the coolant with suspended nano-sized particles in the base fluid is proposed as an alternative to increase heat transfer but minimize flow resistance inside a nuclear reactor core. Due to technical complexities most of the previous studies carried out on heat transfer of suspension of metal oxides in fluids were limited to suspensions with millimeter or micron-sized particles. Such outsized particles may lead to severe problems in heat transfer equipment including increased pressure drop and corrosion and erosion of components and pipe lines. Dramatic advancement in modern science has made it possible to produce ultrafine metallic or nonmetallic particles of nanometer dimension, which has brought a revolutionary change in the research of heat transfer enhancement methods. Due to very tiny particle size and their small volume fraction, problems such as clogging and increased pressure drop are insignificant for nanofluids. Moreover, the relatively large surface area of nanoparticles augments the stability of nanofluid solution and prevents the sedimentation of nanoparticles. Xuan and Roetzel considered two approaches to illustrate
S. Saha Ray
2014-01-01
A very new technique, coupled fractional reduced differential transform, has been implemented to obtain the numerical approximate solution of (2 + 1)-dimensional coupled time fractional burger equations. The fractional derivatives are described in the Caputo sense. By using the present method we can solve many linear and nonlinear coupled fractional differential equations. The obtained results are compared with the exact solutions. Numerical solutions are presented graphically to show the rel...
Directory of Open Access Journals (Sweden)
S. Saha Ray
2014-01-01
Full Text Available A very new technique, coupled fractional reduced differential transform, has been implemented to obtain the numerical approximate solution of (2 + 1-dimensional coupled time fractional burger equations. The fractional derivatives are described in the Caputo sense. By using the present method we can solve many linear and nonlinear coupled fractional differential equations. The obtained results are compared with the exact solutions. Numerical solutions are presented graphically to show the reliability and efficiency of the method.
Tang, Youneng; Valocchi, Albert J.; Werth, Charles J.
2015-03-01
It is a challenge to upscale solute transport in porous media for multispecies bio-kinetic reactions because of incomplete mixing within the elementary volume and because biofilm growth can change porosity and affect pore-scale flow and diffusion. To address this challenge, we present a hybrid model that couples pore-scale subdomains to continuum-scale subdomains. While the pore-scale subdomains involving significant biofilm growth and reaction are simulated using pore-scale equations, the other subdomains are simulated using continuum-scale equations to save computational time. The pore-scale and continuum-scale subdomains are coupled using a mortar method to ensure continuity of solute concentration and flux at the interfaces. We present results for a simplified two-dimensional system, neglect advection, and use dual Monod kinetics for solute utilization and biofilm growth. The results based on the hybrid model are consistent with the results based on a pore-scale model for three test cases that cover a wide range of Damköhler (Da = reaction rate/diffusion rate) numbers for both homogeneous (spatially periodic) and heterogeneous pore structures. We compare results from the hybrid method with an upscaled continuum model and show that the latter is valid only for cases of small Damköhler numbers, consistent with other results reported in the literature.
Numerical solution of system of boundary value problems using B-spline with free parameter
Gupta, Yogesh
2017-01-01
This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.
Influence of karst evolution on solute transport evaluated by process-based numerical modelling
Hubinger, Bernhard; Birk, Steffen
2010-05-01
Karst waters are of major interest in water resources management. Because of their inherent properties karst systems show great vulnerability with regard to contaminants. Karst systems include highly permeable solution conduit networks formed by chemical aggressive water embedded in a fissured matrix. Small initial voids are widened and thus act as preferential passages, where flow is rapid and often turbulent. Water discharging at karst spring originates from different pathways with different residence times. Contaminant transport through conduit pathways is very rapid, whereas flow through the fissured porous matrix is much slower. Thus, on the one hand, pollutants may be rapidly transported and reach high concentrations at the karst spring shortly after their release; on the other hand, the existence of slow flow components may cause the pollution to last for long times. In this work, solute transport properties of karst aquifers are investigated using generic conduit networks of hydraulically connected proto-conduits with initially log-normally distributed apertures in the millimetre range and below. Conduit evolution is modelled by coupling flow, transport, and dissolution processes, whereby single conduits are widened up to the metre range. Thus, different stages of karst evolution can be distinguished. The resulting flow systems provide the basis for modelling advective-dispersive transport of non-reactive solutes through the network of more or less widened (proto-)conduits. The general transport characteristics in karst systems as well as the influence of heterogeneities and structures on solute transport are illustrated for cases of direct injection into the conduit systems at different evolutionary stages. The resulting breakthrough curves typically show several distinct, chronologically shifted peaks with long tailings, which appears to be similar to data from field tracer experiments.
Xing, F.; Masson, R.; Lopez, S.
2017-09-01
This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.
Numerical solution of the problem of selecting the optimum method of operating oil wells
Energy Technology Data Exchange (ETDEWEB)
Skryago, A.M.; Chirikov, L.I.; Fridman, G.Sh.; Kolokolov, A.A.; Panteleyev, G.V.; Terent' yev, S.A.; Zabudskiy, G.G.
1981-01-01
A mathematical model is studied for selecting the optimum method of operating the wells of an oil field, which is a linear Boolean programming problem. It is shown that this problem is equivalent to the generalized packet problem and a single product variant model of sectoral planning. Numerical calculations on the computer using as the initial problem the modified method of E. Balash, for the generalized packet problem the method of M.F. Kazakovaya, and the single product variant problem of sectoral planning the method of A. Ye. Bakhtin, show the greatest effectiveness for the problem studied of A. Ye. Bakhtin's method.
Directory of Open Access Journals (Sweden)
Reza Jalilian
2014-07-01
Full Text Available A Class of new methods based on a septic non-polynomial splinefunction for the numerical solution one-dimensional Bratu's problemare presented. The local truncation errors and the methods of order2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse ofsome band matrixes are obtained which are required in provingthe convergence analysis of the presented method. Associatedboundary formulas are developed. Convergence analysis of thesemethods is discussed. Numerical results are given to illustrate theefficiency of methods.
Numerical Solution of Stokes Flow in a Circular Cavity Using Mesh-free Local RBF-DQ
DEFF Research Database (Denmark)
Kutanaai, S Soleimani; Roshan, Naeem; Vosoughi, A
2012-01-01
This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation...... is applied on a two-dimensional geometry. The obtained results from the numerical simulations are compared with those gained by previous works. Outcomes prove that the current technique is in very good agreement with previous investigations and this fact that RBF-DQ method is an accurate and flexible method...... of derivatives and function approximation of Radial Basis Function. As a result, the method can be used to directly approximate the derivatives of dependent variables on a scattered set of knots. In this study knots were distributed irregularly in the solution domain using the Halton sequences. The method...
Analytical Solutions Using Integral Formulations and Their Coupling with Numerical Approaches.
Morel-Seytoux, Hubert J
2015-01-01
Analytical and numerical approaches have their own distinct domains of merit and application. Unfortunately there has been a tendency to use either one or the other even when their domains overlap. Yet there is definite advantage in combining the two approaches. Being relatively new this emerging technique of combining the approaches is, at this stage, more of an art than a science. In this article we suggest approaches for the combination through simple examples. We also suggest that the integral formulation of the analytical problems may have some advantages over the differential formulation. The differential formulation limits somewhat the range of linear system descriptions that can be applied to a variety of practical problems. On the other hand the integral approach tends to focus attention to overall integrated behavior and properties of the system rather than on minute details. This is particularly useful in the coupling with a numerical model as in practice it generally deals also with only the integrated behavior of the system. The thesis of this article is illustrated with some simple stream-aquifer flow exchange examples. © 2014, National GroundWater Association.
Wael M. Mohamed; Ahmed F. Ghaleb; Enaam K. Rawy; Hassan A.Z. Hassan; Adel A. Mosharafa
2015-01-01
A numerical solution is presented for a one-dimensional, nonlinear boundary-value problem of thermoelasticity with variable volume force and heat supply in a slab. One surface of the body is subjected to a given periodic displacement and Robin thermal condition, while the other is kept fixed and at zero temperature. Other conditions may be equally treated as well. The volume force and bulk heating simulate the effect of a beam of hot particles infiltrating the medium. The present study is a c...
Sternovsky, Z; Downum, K; Robertson, S
2004-08-01
A kinetic model of the plasma-sheath problem is presented that includes the effects of charge-exchange collisions of the ion. The collisions are modeled as a sink for accelerated ions and as a source of cold ions. Solutions are obtained by numerical integration of Poisson's equation from a point near the plasma midplane to the wall. In the quasineutral region, these solutions agree with earlier analytic work. As the mean free path is decreased, the current density at the wall decreases and the potential profile in the quasineutral region shows a smooth transition from a parabolic profile to a nearly cubic profile determined by the ion mobility. An approximate expression is found for the ion flux to the wall in the collisional limit.
Directory of Open Access Journals (Sweden)
A. Mushtaq
2016-01-01
Full Text Available Present work studies the well-known Sakiadis flow of Maxwell fluid along a moving plate in a calm fluid by considering the Cattaneo-Christov heat flux model. This recently developed model has the tendency to describe the characteristics of relaxation time for heat flux. Some numerical local similarity solutions of the associated problem are computed by two approaches namely (i the shooting method and (ii the Keller-box method. The solution is dependent on some interesting parameters which include the viscoelastic fluid parameter β, the dimensionless thermal relaxation time γ and the Prandtl number Pr. Our simulations indicate that variation in the temperature distribution with an increase in local Deborah number γ is non-monotonic. The results for the Fourier’s heat conduction law can be obtained as special cases of the present study.
Salama, Amgad
2015-06-01
In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.
Energy Technology Data Exchange (ETDEWEB)
Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)
1997-12-31
This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)
Gunzburger, M. D.; Nicolaides, R. A.
1986-01-01
Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.
Bezier Curves Based Numerical Solutions of Delay Systems with Inverse Time
Directory of Open Access Journals (Sweden)
F. Ghomanjani
2014-01-01
Full Text Available This paper applied, for the first time, the Bernstein’s approximation on delay differential equations and delay systems with inverse delay that models these problems. The direct algorithm is given for solving this problem. The delay function and inverse time function are expanded by the Bézier curves. The Bézier curves are chosen as piecewise polynomials of degree n, and the Bézier curves are determined on any subinterval by n+1 control points. The approximated solution of delay systems containing inverse time is derived. To validate accuracy of the present algorithm, some examples are solved.
Numerical solution of time- and space-fractional coupled Burgers’ equations via homotopy algorithm
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Jagdev Singh
2016-06-01
Full Text Available In this paper, we constitute a homotopy algorithm basically extension of homotopy analysis method with Laplace transform, namely q-homotopy analysis transform method to solve time- and space-fractional coupled Burgers’ equations. The suggested technique produces many more opportunities by appropriate selection of auxiliary parameters ℏ and n(n⩾1 to solve strongly nonlinear differential equations. The proposed technique provides ℏ and n-curves, which describe that the convergence range is not a local point effects and finds elucidated series solution that makes it superior than HAM and other analytical techniques.
Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
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Nowak Tomasz Karol
2014-06-01
Full Text Available This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
Numerical solutions of anharmonic vibration of BaO and SrO molecules
Pramudito, Sidikrubadi; Sanjaya, Nugraha Wanda; Sumaryada, Tony
2016-03-01
The Morse potential is a potential model that is used to describe the anharmonic behavior of molecular vibration between atoms. The BaO and SrO molecules, which are two almost similar diatomic molecules, were investigated in this research. Some of their properties like the value of the dissociation energy, the energy eigenvalues of each energy level, and the profile of the wavefunctions in their correspondence vibrational states were presented in this paper. Calculation of the energy eigenvalues and plotting the wave function's profiles were performed using Numerov method combined with the shooting method. In general we concluded that the Morse potential solved with numerical methods could accurately produce the vibrational properties and the wavefunction behavior of BaO and SrO molecules from the ground state to the higher states close to the dissociation level.
Directory of Open Access Journals (Sweden)
Haixiong Yu
2014-01-01
Full Text Available We apply a lumped mass finite element to approximate Dirichlet problems for nonsmooth elliptic equations. It is proved that the lumped mass FEM approximation error in energy norm is the same as that of standard piecewise linear finite element approximation. Under the quasi-uniform mesh condition and the maximum angle condition, we show that the operator in the finite element problem is diagonally isotone and off-diagonally antitone. Therefore, some monotone convergent algorithms can be used. As an example, we prove that the nonsmooth Newton-like algorithm is convergent monotonically if Gauss-Seidel iteration is used to solve the Newton's equations iteratively. Some numerical experiments are presented.
Numerical solution of the Black-Scholes equation using cubic spline wavelets
Černá, Dana
2016-12-01
The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.
Numerical solution of the problem of detecting diffractors in a complex acoustic media
Danilin, Alexander N.; Pestov, Leonid N.
2017-11-01
One of the most effective methods for detecting weak scattering objects (diffractors) associated with cracked-cavernous hydrocarbon reservoirs is the CSP (Common Scattering Point) method [1]. This method is the most effective for weakly inhomogeneous media. The CSP method can be supplemented by a preliminary continuation of the wave field to a certain depth for strongly inhomogeneous medium. In this paper we use Reverse Time Datuming (RTD) procedure for this purpose [2, 3, 4]. The new CSP-RTD method is based on both CSP and RTD methods for determining deep-seated diffractors in complex acoustic medium. The results of numerical studies of CSP-RTD method for a complex acoustic model is presented. The comparison of CSP-RTD method and RTM method is also presented.
Numerical solutions of the momentum equations for the lower overshoot layer
Marik, D.; Petrovay, K.
2001-01-01
The lower overshooting layer, which plays an important role in the dynamo mechanism, is one of the least known regions of the Sun. The most promising way to model this region is the Reynolds-stress method. In this paper we determine the radial distribution of the turbulent kinetic energy k, the mean square relative temperature fluctuation q, the normalized energy flux J, and the energy dissipation rate ɛ. We present solutions in the case of a simple k-ɛ model and in the case of solving all four differential equations using various Δ∇ distributions (temperature stratifications). We use a diffusive approximation for the nonlocal fluxes ("Xiong's closure"), considering the case of both strong and weak nonlocality. The resulting profiles of k and ɛ are found to be approximately linear and the profiles of the turbulent lengths and time scales l and τ are also similar for different cases. The shapes of these profiles thus seem to be robust properties of the solution, with little sensitivity to the particular parameter values and background stratification assumed. In contrast, we find that the penetration depth depends rather sensitively on the slope of the Δ∇ curve and on the strength of nonlocality assumed.
SOLA-DM: A numerical solution algorithm for transient three-dimensional flows
Energy Technology Data Exchange (ETDEWEB)
Wilson, T.L.; Nichols, B.D.; Hirt, C.W.; Stein, L.R.
1988-02-01
SOLA-DM is a three-dimensional time-explicit, finite-difference, Eulerian, fluid-dynamics computer code for solving the time-dependent incompressible Navier-Stokes equations. The solution algorithm (SOLA) evolved from the marker-and-cell (MAC) method, and the code is highly vectorized for efficient performance on a Cray computer. The computational domain is discretized by a mesh of parallelepiped cells in either cartesian or cylindrical geometry. The primary hydrodynamic variables for approximating the solution of the momentum equations are cell-face-centered velocity components and cell-centered pressures. Spatial accuracy is selected by the user to be first or second order; the time differencing is first-order accurate. The incompressibility condition results in an elliptic equation for pressure that is solved by a conjugate gradient method. Boundary conditions of five general types may be chosen: free-slip, no-slip, continuative, periodic, and specified pressure. In addition, internal mesh specifications to model obstacles and walls are provided. SOLA-DM also solves the equations for discrete particle dynamics, permitting the transport of marker particles or other solid particles through the fluid to be modeled. 7 refs., 7 figs.
Directory of Open Access Journals (Sweden)
J. Vanderborght
1997-01-01
Full Text Available Abstract: Field-scale solute dispersion is determined by water flow heterogeneity which results from spatial variability of soil hydraulic properties and soil moisture state. Measured variabilities of soil hydraulic properties are highly sensitive to the experimental method. Field-scale dispersion derived from leaching experiments in a macroporous loam soil was compared with field-scale dispersion obtained with numerical simulations in heterogeneous random fields. Four types of random fields of hydraulic properties having statistical properties derived from four different types of laboratory measurements were considered. Based on this comparison, the measurement method depicting heterogeneities of hydraulic properties most relevant to field-scale solute transport was identified. For unsaturated flow, the variability of the hydraulic conductivity characteristic measured on a small soil volume was the most relevant parameter. For saturated flow, simulated dispersion underestimated the measured dispersion and it was concluded that heterogeneity of macroscopic hydraulic properties could not represent solute flow heterogeneity under these flow conditions. Field-scale averaged solute concentrations depend both on the detection method and the averaging procedure. Flux-averaged concentrations (relevant to practical applications differ from volume-averaged or resident concentrations (easy to measure, especially when water flow is more heterogeneous. Simulated flux and resident concentrations were subsequently used to test two simple one-dimensional transport models in predicting flux concentrations when they are calibrated on resident concentrations. In the first procedure, solute transport in a heterogeneous soil is represented by a 1-D convection dispersion process. The second procedure was based on the relation between flux and resident concentrations for a stochastic convective process. Better predictions of flux concentrations were obtained using
Hong, Sung-Jei; Kim, Jong-Woong; Kim, Yong-Hoon
2014-12-01
In this study, solution-processed hybrid structure transparent conductors consisting of silver nanowires (AgNWs) and indium-tin-oxide nanoparticle (ITO-NP) layers are investigated. Fabricated transparent conductors had stacked structures of ITO-NP/AgNW and ITO-NP/AgNW/ITO-NP, and a successful integration was possible on glass substrates. Compared to a single-layered ITO-NP film which has a sheet resistance value of 1.31 k Ω/⟂, a remarkable enhancement in sheet resistance was achieved from the hybrid structures, showing sheet resistance values of 44.74 Ω/⟂ and 28.07 Ω/⟂ for ITO-NP/AgNW and ITO-NP/AgNW/ITO-NP structures, respectively. In addition, the ITO-NP/AgNW/ITO-NP triple-layered transparent conductor showed greatly enhanced thermal stability in terms of sheet resistance and transmittance against a high-temperature environment up to 300 degrees C. Based on these results, it can be suggested that the hybrid structure has advantages of enhancing both electrical properties of ITO-NP layer and thermal stability of AgNW layer, and we believe the hybrid structure transparent conductors can be a suitable option for applications which require high electrical conductivity, transmittance, and thermal stability.
Redox levels in aqueous solution: Effect of van der Waals interactions and hybrid functionals.
Ambrosio, Francesco; Miceli, Giacomo; Pasquarello, Alfredo
2015-12-28
We investigate redox levels in aqueous solution using a combination of ab initio molecular dynamics (MD) simulations and thermodynamic integration methods. The molecular dynamics are performed with both the semilocal Perdew-Burke-Ernzerhof functional and a nonlocal functional (rVV10) accounting for van der Waals (vdW) interactions. The band edges are determined through three different schemes, namely, from the energy of the highest occupied and of the lowest unoccupied Kohn-Sham states, from total-energy differences, and from a linear extrapolation of the density of states. It is shown that the latter does not depend on the system size while the former two are subject to significant finite-size effects. For the redox levels, we provide a formulation in analogy to the definition of charge transition levels for defects in crystalline materials. We consider the H(+)/H2 level defining the standard hydrogen electrode, the OH(-)/OH(∗) level corresponding to the oxidation of the hydroxyl ion, and the H2O/OH(∗) level for the dehydrogenation of water. In spite of the large structural modifications induced in liquid water, vdW interactions do not lead to any significant structural effect on the calculated band gap and band edges. The effect on the redox levels is also small since the solvation properties of ionic species are little affected by vdW interactions. Since the electronic properties are not significantly affected by the underlying structural properties, it is justified to perform hybrid functional calculations on the configurations of our MD simulations. The redox levels calculated as a function of the fraction α of Fock exchange are found to remain constant, reproducing a general behavior previously observed for charge transition levels of defects. Comparison with experimental values shows very good agreement. At variance, the band edges and the band gap evolve linearly with α. For α ≃ 0.40, we achieve a band gap, band-edge positions, and redox levels in
Redox levels in aqueous solution: Effect of van der Waals interactions and hybrid functionals
Ambrosio, Francesco; Miceli, Giacomo; Pasquarello, Alfredo
2015-12-01
We investigate redox levels in aqueous solution using a combination of ab initio molecular dynamics (MD) simulations and thermodynamic integration methods. The molecular dynamics are performed with both the semilocal Perdew-Burke-Ernzerhof functional and a nonlocal functional (rVV10) accounting for van der Waals (vdW) interactions. The band edges are determined through three different schemes, namely, from the energy of the highest occupied and of the lowest unoccupied Kohn-Sham states, from total-energy differences, and from a linear extrapolation of the density of states. It is shown that the latter does not depend on the system size while the former two are subject to significant finite-size effects. For the redox levels, we provide a formulation in analogy to the definition of charge transition levels for defects in crystalline materials. We consider the H+/H2 level defining the standard hydrogen electrode, the OH-/OH∗ level corresponding to the oxidation of the hydroxyl ion, and the H2O/OH∗ level for the dehydrogenation of water. In spite of the large structural modifications induced in liquid water, vdW interactions do not lead to any significant structural effect on the calculated band gap and band edges. The effect on the redox levels is also small since the solvation properties of ionic species are little affected by vdW interactions. Since the electronic properties are not significantly affected by the underlying structural properties, it is justified to perform hybrid functional calculations on the configurations of our MD simulations. The redox levels calculated as a function of the fraction α of Fock exchange are found to remain constant, reproducing a general behavior previously observed for charge transition levels of defects. Comparison with experimental values shows very good agreement. At variance, the band edges and the band gap evolve linearly with α. For α ≃ 0.40, we achieve a band gap, band-edge positions, and redox levels in overall
A numerical solution for the entrance region of non-newtonian flow in annuli
Directory of Open Access Journals (Sweden)
Maia M.C.A.
2003-01-01
Full Text Available Continuity and momentum equations applied to the entrance region of an axial, incompressible, isothermal, laminar and steady flow of a power-law fluid in a concentric annulus, were solved by a finite difference implicit method. The Newtonian case was solved used for validation of the method and then compared to reported results. For the non-Newtonian case a pseudoplastic power-law model was assumed and the equations were transformed to obtain a pseudo-Newtonian system which enabled its solution using the same technique as that used for the Newtonian case. Comparison of the results for entrance length and pressure drop with those available in the literature showed a qualitative similarity, but significant quantitative differences. This can be attributed to the differences in entrance geometries and the definition of asymptotic entrance length.
DEFF Research Database (Denmark)
Kaiser, Franz-Joachim; Bassler, Niels; Tölli, Heikki
2012-01-01
. In this study the effect of the underlying dose distribution on columnar recombination, a quantitative model for initial recombination,is investigated. Material and Methods Jaffe’s theory, formulated in 1913 quantifies initial recombination by elemental processes, providing an analytical (closed) solution. Here...... in the assessment of the saturation current or charge is suggested by the data. Conclusion The established model of columnar recombination reproduces the experimental data well, whereas the extentions using track structure models do not show such an agreement. Additionally, the effect of initial recombination...... on the saturation curve (i.e. Jaffe plot) does not follow a linear behavior as suggested by current dosimetry protocols, therefore higher order corrections (such as the investigated ones) might be necessary....
Light scattering and absorption by space weathered planetary bodies: Novel numerical solution
Markkanen, Johannes; Väisänen, Timo; Penttilä, Antti; Muinonen, Karri
2017-10-01
Airless planetary bodies are exposed to space weathering, i.e., energetic electromagnetic and particle radiation, implantation and sputtering from solar wind particles, and micrometeorite bombardment.Space weathering is known to alter the physical and chemical composition of the surface of an airless body (C. Pieters et al., J. Geophys. Res. Planets, 121, 2016). From the light scattering perspective, one of the key effects is the production of nanophase iron (npFe0) near the exposed surfaces (B. Hapke, J. Geophys. Res., 106, E5, 2001). At visible and ultraviolet wavelengths these particles have a strong electromagnetic response which has a major impact on scattering and absorption features. Thus, to interpret the spectroscopic observations of space-weathered asteroids, the model should treat the contributions of the npFe0 particles rigorously.Our numerical approach is based on the hierarchical geometric optics (GO) and radiative transfer (RT). The modelled asteroid is assumed to consist of densely packed silicate grains with npFe0 inclusions. We employ our recently developed RT method for dense random media (K. Muinonen, et al., Radio Science, submitted, 2017) to compute the contributions of the npFe0 particles embedded in silicate grains. The dense media RT method requires computing interactions of the npFe0 particles in the volume element for which we use the exact fast superposition T-matrix method (J. Markkanen, and A.J. Yuffa, JQSRT 189, 2017). Reflections and refractions on the grain surface and propagation in the grain are addressed by the GO. Finally, the standard RT is applied to compute scattering by the entire asteroid.Our numerical method allows for a quantitative interpretation of the spectroscopic observations of space-weathered asteroids. In addition, it may be an important step towards more rigorous a thermophysical model of asteroids when coupled with the radiative and conductive heat transfer techniques.Acknowledgments. Research supported by
Chavez, Gustavo Ivan
2017-07-10
This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST\\'s Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.
Public-domain-software solution to data-access problems for numerical modelers
Jenter, Harry; Signell, Richard
1992-01-01
Unidata's network Common Data Form, netCDF, provides users with an efficient set of software for scientific-data-storage, retrieval, and manipulation. The netCDF file format is machine-independent, direct-access, self-describing, and in the public domain, thereby alleviating many problems associated with accessing output from large hydrodynamic models. NetCDF has programming interfaces in both the Fortran and C computer language with an interface to C++ planned for release in the future. NetCDF also has an abstract data type that relieves users from understanding details of the binary file structure; data are written and retrieved by an intuitive, user-supplied name rather than by file position. Users are aided further by Unidata's inclusion of the Common Data Language, CDL, a printable text-equivalent of the contents of a netCDF file. Unidata provides numerous operators and utilities for processing netCDF files. In addition, a number of public-domain and proprietary netCDF utilities from other sources are available at this time or will be available later this year. The U.S. Geological Survey has produced and is producing a number of public-domain netCDF utilities.
Numerical solution of the asymmetric water impact of a wedge in three degrees of freedom
Ghazizade-Ahsaee, H.; Nikseresht, A. H.
2013-06-01
Impact problems associated with water entry have important applications in various aspects of naval architecture and ocean engineering. Estimation of hydrodynamic impact forces especially during the first instances after the impact is very important and is of interest. Since the estimation of hydrodynamic impact load plays an important role in safe design and also in evaluation of structural weight and costs, it is better to use a reliable and accurate prediction method instead of a simple estimation resulted by analyzing methods. In landing of flying boats, some phenomena such as weather conditions and strong winds can cause asymmetric instead of symmetric descent. In this paper, a numerical simulation of the asymmetric impact of a wedge, as the step of a flying boat, considering dynamic equations in two-phase flow is taken into account. The dynamic motion of the wedge in two-phase flow is solved based on finite volume method with volume of fluid (VOF) scheme considering dynamic equations. Then the effects of different angles of impact and water depth on the velocity change and slamming forces in an asymmetric impact are investigated. The comparison between the simulation results and experimental data verifies the accuracy of the method applied in the present study.
Ab initio theory of superconductivity in a magnetic field. II. Numerical solution
Linscheid, A.; Sanna, A.; Gross, E. K. U.
2015-07-01
We numerically investigate the spin density functional theory for superconductors (SpinSCDFT) and the approximated exchange-correlation functional, derived and presented in the preceding Paper I [A. Linscheid et al., Phys. Rev. B 92, 024505 (2015), 10.1103/PhysRevB.92.024505]. As a test system, we employ a free-electron gas featuring an exchange splitting, a phononic pairing field, and a Coulomb repulsion. SpinSCDFT results are compared with Sarma, the Bardeen-Cooper-Schrieffer theory, and with an Eliashberg type of approach. We find that the spectrum of the superconducting Kohn-Sham SpinSCDFT system is not in agreement with the true quasiparticle structure. Therefore, starting from the Dyson equation, we derive a scheme that allows to compute the many-body excitations of the superconductor and represents the extension to superconductivity of the G0W0 method in band-structure theory. This superconducting G0W0 method vastly improves the predicted spectra.
Numerical solution of multiband k.p model for tunnelling in type-II heterostructures
Directory of Open Access Journals (Sweden)
A.E. Botha
2010-01-01
Full Text Available A new and very general method was developed for calculating the charge and spin-resolved electron tunnelling in type-II heterojunctions. Starting from a multiband k.p description of the bulk energy-band structure, a multiband k.p Riccati equation was derived. The reflection and transmission coefficients were obtained for each channel by integrating the Riccati equation over the entire heterostructure. Numerical instability was reduced through this method, in which the multichannel log-derivative of the envelope function matrix, rather than the envelope function itself, was propagated. As an example, a six-band k.p Hamiltonian was used to calculate the current-voltage characteristics of a 10-nm wide InAs/ GaSb/InAs single quantum well device which exhibited negative differential resistance at room temperature. The calculated current as a function of applied (bias voltage was found to be in semiquantitative agreement with the experiment, a result which indicated that inelastic transport mechanisms do not contribute significantly to the valley currents measured in this particular device.
Numerical Solution and it's Analysis during Solar Drying of Green Peas
Godireddy, Arunsandeep; Lingayat, Abhay; Naik, Razat Kumar; Chandramohan, V. P.; Raju, V. Rajesh Kanan
2017-08-01
A mathematical model is developed for solar drying of green peas (Botanical name: Pisum Sativum). The problem is solved assuming the shape of the green peas is spherical. The governing transient mass transfer equation is discretized into finite difference scheme. The time marching is performed by implicit scheme. The governing equations and boundary conditions are non-dimensionalized to get generic results. The product in the chamber is in contact with air which is heated by solar energy, so the boundary conditions of third kind (convective boundary conditions) are considered. By space and time discretization a set of algebraic equations are generated and these algebraic equations are solved by tridiagonal matrix algorithm. A computer code is developed in MATLAB in order to compute the transient moisture content distribution inside the product. Center point, boundary and mean moisture of green peas are estimated at different temperatures and drying time. Present numerical result is compared with experimental result from literature and it was found that there is a good agreement of results. The drying time is predicted for how quickly the mean moisture of green peas is reached to 50, 40, 30, 20 and 10% of its initial moisture corresponding to different temperatures.
Directory of Open Access Journals (Sweden)
Sara eDe Faveri
2014-04-01
Full Text Available The use of implants that allow chronic electrical stimulation and recording in the brain of human patients is currently limited by a series of events that cause the deterioration over time of both the electrode surface and the surrounding tissue. The main reason of failure is the tissue inflammatory reaction that eventually causes neuronal loss and glial encapsulation, resulting in a progressive increase of the electrode-electrolyte impedance. Here, we describe a new method to create bio-inspired electrodes to mimic the mechanical properties and biological composition of the host tissue. This combination has a great potential to increase the implant lifetime by reducing tissue reaction and improving electrical coupling. Our method implies coating the electrode with reprogrammed neural or glial cells encapsulated within a hydrogel layer. We chose fibrin as a hydrogel and primary hippocampal neurons or astrocytes from rat brain as cellular layer. We demonstrate that fibrin coating is highly biocompatible, forms uniform coatings of controllable thickness, does not alter the electrochemical properties of the microelectrode and allows good quality recordings. Moreover, it reduces the amount of host reactive astrocytes - over time - compared to a bare wire and is fully reabsorbed by the surrounding tissue within 7 days after implantation, avoiding the common problem of hydrogels swelling. Both astrocytes and neurons could be successfully grown onto the electrode surface within the fibrin hydrogel without altering the electrochemical properties of the microelectrode. This bio-hybrid device has therefore a good potential to improve the electrical integration at the neuron-electrode interface and support the long-term success of neural prostheses.
De Faveri, Sara; Maggiolini, Emma; Miele, Ermanno; De Angelis, Francesco; Cesca, Fabrizia; Benfenati, Fabio; Fadiga, Luciano
2014-01-01
The use of implants that allow chronic electrical stimulation and recording in the brain of human patients is currently limited by a series of events that cause the deterioration over time of both the electrode surface and the surrounding tissue. The main reason of failure is the tissue inflammatory reaction that eventually causes neuronal loss and glial encapsulation, resulting in a progressive increase of the electrode-electrolyte impedance. Here, we describe a new method to create bio-inspired electrodes to mimic the mechanical properties and biological composition of the host tissue. This combination has a great potential to increase the implant lifetime by reducing tissue reaction and improving electrical coupling. Our method implies coating the electrode with reprogrammed neural or glial cells encapsulated within a hydrogel layer. We chose fibrin as a hydrogel and primary hippocampal neurons or astrocytes from rat brain as cellular layer. We demonstrate that fibrin coating is highly biocompatible, forms uniform coatings of controllable thickness, does not alter the electrochemical properties of the microelectrode and allows good quality recordings. Moreover, it reduces the amount of host reactive astrocytes - over time - compared to a bare wire and is fully reabsorbed by the surrounding tissue within 7 days after implantation, avoiding the common problem of hydrogels swelling. Both astrocytes and neurons could be successfully grown onto the electrode surface within the fibrin hydrogel without altering the electrochemical properties of the microelectrode. This bio-hybrid device has therefore a good potential to improve the electrical integration at the neuron-electrode interface and support the long-term success of neural prostheses.
Energy Technology Data Exchange (ETDEWEB)
Ha, Tae-Jun [Department of Electronic Materials Engineering, Kwangwoon University, Seoul 139-701 (Korea, Republic of)
2014-07-28
This study presents a promising approach to realize low-voltage (<3 V) organic thin-film transistors (OTFTs) exhibiting improved electrical and optical stability. Such device performance results from the use of solution-processed hybrid bilayer gate dielectrics consisting of zirconium dioxide (high-k dielectric) and amorphous fluoropolymer, CYTOP{sup ®} (low-k dielectric). Employing a very thin amorphous fluoropolymer film reduces interfacial defect-states by repelling water molecules and other aqueous chemicals from an organic semiconductor active layer due to the hydrophobic surface-property. The chemically clean interface, stemming from decrease in density of trap states improves all the key device properties such as field-effect mobility, threshold voltage, and sub-threshold swing. Furthermore, degradation by electrical bias-stress and photo-induced hysteresis were suppressed in OTFTs employing hybrid bilayer gate dielectrics.
Directory of Open Access Journals (Sweden)
Rita B. Figueira
2017-03-01
Full Text Available Hybrid sol-gel coatings, named U(X:TEOS, based on ureasilicate matrices (U(X enriched with tetraethoxysilane (TEOS, were synthesized. The influence of TEOS addition was studied on both the structure of the hybrid sol-gel films as well as on the electrochemical properties. The effect of TEOS on the structure of the hybrid sol-gel films was investigated by solid state Nuclear Magnetic Resonance. The dielectric properties of the different materials were investigated by electrochemical impedance spectroscopy. The corrosion behavior of the hybrid coatings on HDGS was studied in chloride-contaminated simulated concrete pore solutions (SCPS by polarization resistance measurements. The roughness of the HDGS coated with hybrids was also characterized by atomic force microscopy. The structural characterization of the hybrid materials proved the effective reaction between Jeffamine® and 3-isocyanate propyltriethoxysilane (ICPTES and indicated that the addition of TEOS does not seem to affect the organic structure or to increase the degree of condensation of the hybrid materials. Despite the apparent lack of influence on the hybrids architecture, the polarization resistance measurements confirmed that TEOS addition improves the corrosion resistance of the hybrid coatings (U(X:TEOS in chloride-contaminated SCPS when compared to samples prepared without any TEOS (U(X. This behavior could be related to the decrease in roughness of the hybrid coatings (due TEOS addition and to the different metal coating interaction resulting from the increase of the inorganic component in the hybrid matrix.
Directory of Open Access Journals (Sweden)
Basuki Widodo
2012-02-01
Full Text Available Corrosion process is a natural case that happened at the various metals, where the corrosion process in electrochemical can be explained by using galvanic cell. The iron corrosion process is based on the acidity degree (pH of a condensation, iron concentration and condensation temperature of electrolyte. Those are applied at electrochemistry cell. The iron corrosion process at this electrochemical cell also able to generate electrical potential and electric current during the process takes place. This paper considers how to build a mathematical model of iron corrosion, electrical potential and electric current. The mathematical model further is solved using the finite element method. This iron corrosion model is built based on the iron concentration, condensation temperature, and iteration time applied. In the electric current density model, the current based on electric current that is happened at cathode and anode pole and the iteration time applied. Whereas on the potential electric model, it is based on the beginning of electric potential and the iteration time applied. The numerical results show that the part of iron metal, that is gristle caused by corrosion, is the part of metal that has function as anode and it has some influences, such as time depth difference, iron concentration and condensation temperature on the iron corrosion process and the sum of reduced mass during corrosion process. Moreover, difference influence of time and beginning electric potential has an effect on the electric potential, which emerges during corrosion process at the electrochemical cell. Whereas, at the electrical current is also influenced by difference of depth time and condensation temperature applied.Keywords: Iron Corrosion, Concentration of iron, Electrochemical Cell and Finite Element Method
An Experimenting Field Approach for the Numerical Solution of Multiphase Flow in Porous Media.
Salama, Amgad; Sun, Shuyu; Bao, Kai
2016-03-01
In this work, we apply the experimenting pressure field technique to the problem of the flow of two or more immiscible phases in porous media. In this technique, a set of predefined pressure fields are introduced to the governing partial differential equations. This implies that the velocity vector field and the divergence at each cell of the solution mesh can be determined. However, since none of these fields is the true pressure field entailed by the boundary conditions and/or the source terms, the divergence at each cell will not be the correct one. Rather the residue which is the difference between the true divergence and the calculated one is obtained. These fields are designed such that these residuals are used to construct the matrix of coefficients of the pressure equation and the right-hand side. The experimenting pressure fields are generated in the solver routine and are fed to the different routines, which may be called physics routines, which return to the solver the elements of the matrix of coefficients. Therefore, this methodology separates the solver routines from the physics routines and therefore results in simpler, easy to construct, maintain, and update algorithms. © 2015, National Ground Water Association.
Some strange numerical solutions of the non-stationary Navier-Stokes equations in pipes
Energy Technology Data Exchange (ETDEWEB)
Rummler, B.
2001-07-01
A general class of boundary-pressure-driven flows of incompressible Newtonian fluids in three-dimensional pipes with known steady laminar realizations is investigated. Considering the laminar velocity as a 3D-vector-function of the cross-section-circle arguments, we fix the scale for the velocity by the L{sub 2}-norm of the laminar velocity. The usual new variables are introduced to get dimension-free Navier-Stokes equations. The characteristic physical and geometrical quantities are subsumed in the energetic Reynolds number Re and a parameter {psi}, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form u=u{sub L}+u, where u{sub L} is the scaled laminar velocity and periodical conditions in center-line-direction are prescribed for u. An autonomous system (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction is got by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u. The finite-dimensional approximations u{sub N({lambda}}{sub )} of u are defined in the usual way. (orig.)
Directory of Open Access Journals (Sweden)
Alexander Jerabek
2012-10-01
Full Text Available This paper describes an implementation of a hybrid solution for improving the library's proxy service by integrating Shibboleth and ExLibris' Aleph’s X-server using a proxy server running both EZproxy and Squid applications. We will describe in detail the hybrid solution of a proxy service within the context of our institution and explain how this service improves the user experience. We will explain how we developed and implemented this solution with a minimum of development cost and describe some of the preliminary empirical research undertaken. The main benefit of this solution is that instead of relying on e-resource vendors to become Shibboleth-compliant, we are able to prepare and deploy a Shibboleth-ready environment while granting our patrons reliable and stable access to e-resources via different types of connections. As of December 2011, the hybrid solution is running in production.
Viral Hybrid Vectors for Somatic Integration - Are They the Better Solution?
Directory of Open Access Journals (Sweden)
Anja Ehrhardt
2009-12-01
Full Text Available The turbulent history of clinical trials in viral gene therapy has taught us important lessons about vector design and safety issues. Much effort was spent on analyzing genotoxicity after somatic integration of therapeutic DNA into the host genome. Based on these findings major improvements in vector design including the development of viral hybrid vectors for somatic integration have been achieved. This review provides a state-of-the-art overview of available hybrid vectors utilizing viruses for high transduction efficiencies in concert with various integration machineries for random and targeted integration patterns. It discusses advantages but also limitations of each vector system.
Directory of Open Access Journals (Sweden)
José Miguel Vargas-Félix
2012-11-01
Full Text Available The Finite Element Method (FEM is used to solve problems like solid deformation and heat diffusion in domains with complex geometries. This kind of geometries requires discretization with millions of elements; this is equivalent to solve systems of equations with sparse matrices and tens or hundreds of millions of variables. The aim is to use computer clusters to solve these systems. The solution method used is Schur substructuration. Using it is possible to divide a large system of equations into many small ones to solve them more efficiently. This method allows parallelization. MPI (Message Passing Interface is used to distribute the systems of equations to solve each one in a computer of a cluster. Each system of equations is solved using a solver implemented to use OpenMP as a local parallelization method.The Finite Element Method (FEM is used to solve problems like solid deformation and heat diffusion in domains with complex geometries. This kind of geometries requires discretization with millions of elements; this is equivalent to solve systems of equations with sparse matrices and tens or hundreds of millions of variables. The aim is to use computer clusters to solve these systems. The solution method used is Schur substructuration. Using it is possible to divide a large system of equations into many small ones to solve them more efficiently. This method allows parallelization. MPI (Message Passing Interface is used to distribute the systems of equations to solve each one in a computer of a cluster. Each system of equations is solved using a solver implemented to use OpenMP as a local parallelization method.
Naganthran, Kohilavani; Nazar, Roslinda
2017-08-01
In this study, the influence of the first order chemical reaction towards the magnetohydrodynamics (MHD) stagnation-point boundary layer flow past a permeable stretching/shrinking surface (sheet) is considered numerically. The governing boundary layer equations are transformed into a system of ordinary differential equations from the system of partial differential equations by using a proper similarity transformation so that it can be solved numerically by the "bvp4c" function in Matlab software. The main numerical solutions are presented graphically and discussed in the relevance of the governing parameters. It is found that dual solutions exist when the sheet is stretched and shrunk. Stability analysis is done to determine which solution is stable and valid physically. The results of the stability analysis show that the first solution (upper branch) is physically stable and realizable while the second solution (lower branch) is impracticable.
Solution-processed MoO3:PEDOT:PSS hybrid hole transporting layer for inverted polymer solar cells.
Wang, Yiling; Luo, Qun; Wu, Na; Wang, Qiankun; Zhu, Hongfei; Chen, Liwei; Li, Yan-Qing; Luo, Liqiang; Ma, Chang-Qi
2015-04-08
Solution-processed organic-inorganic hybrids composing of MoO3 nanoparticles and PEDOT:PSS were developed for use in inverted organic solar cells as hole transporting layer (HTL). The hybrid MoO3:PEDOT:PSS inks were prepared by simply mixing PEDOT:PSS aqueous and MoO3 ethanol suspension together. A core-shell structure was proposed in the MoO3:PEDOT:PSS hybrid ink, where PEDOT chains act as the core and MoO3 nanoparticles connected with PSS chains act as the composite shell. The mixing with PEDOT:PSS suppressed the aggregation of MoO3 nanoparticles, which led to a smoother surface. In addition, since the hydrophilic PSS chains were passivated through preferentially connection with MoO3, the stronger adhesion between MoO3 nanoparticles and the photoactive layer improved the film forming ability of the MoO3:PEDOT:PSS hybrid ink. The MoO3:PEDOT:PSS hybrid HTL can therefore be feasibly deposited onto the hydrophobic photoactive polymer layer without any surface treatment. The use of the MoO3:PEDOT:PSS hybrid HTL resulted in the optimized P3HT:PC61BM- and PTB7:PC61BM-based inverted organic solar cells reaching highest power conversion efficiencies of 3.29% and 5.92%, respectively, which were comparable with that of the control devices using thermally evaporated MoO3 HTL (3.05% and 6.01%, respectively). Furthermore, less HTL thickness dependence of device performance was found for the hybrid HTL-based devices, which makes it more compatible with roll-to-roll printing process. In the end, influence of the blend ratio of MoO3 to PEDOT:PSS on photovoltaic performance and device stability was studied carefully, results indicated that the device performance would decrease with the increase of MoO3 blended ratio, whereas the long-term stability was improved.
Numerical solution of the start-up of well drilling fluid flows
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Gabriel Merhy de; Negrao, Cezar Otaviano Ribeiro; Franco, Admilson Teixeira [UTFPR - Federal University of Technology - Parana - Curitiba, PR (Brazil)], e-mails: gabrielm@utfpr.edu.br, negrao@utfpr.edu.br, admilson@utfpr.edu.br; Martins, Andre Leibsohn; Gandelman, Roni Abensur [TEP/CENPES - PETROBRAS S/A, Rio de Janeiro, RJ (Brazil)], e-mails: aleibsohn@petrobras.com.br, roniag@petrobras.com.br
2010-07-01
The drilling fluid is designed to build up a gel-like structure, when at rest, in order to avoid cuttings to drop at the bore bottom and therefore to prevent the bit obstruction. As consequence, high pressures, which can be larger than the formation pressure and can damage the well, are needed to break up the gel when circulation resumes. Due to its thixotropic effect, the gel viscosity remains high for a while after the circulation restarts. The gelation may have significant importance, specially, in deep waters where high pressures and low temperatures take place. The current work presents a compressible transient flow model of the start-up flow of drilling fluids, in order to predict borehole pressures. The model comprises one-dimensional conservation equations of mass and momentum and one state equation for the calculation of the fluid density as a function of the pressure. The considered geometry is a concentric annular pipe of length L. Its internal diameter is D1 and external one, D2. For a circular pipe, the internal diameter is made equal to zero. The main difference from previous model was the type of boundary condition: Constant flow rate at the pipe inlet rather than the constant pressure. Both Newtonian and non-Newtonian Bingham fluid flows are considered. The governing equations are discretized by the Finite Volume Method using the fully implicit formulation and the first-order upwind scheme. The resulting non-linear algebraic equations are iteratively solved. The model results were corroborated with an analytical solution for Newtonian flows. Case studies are conducted to evaluate the effect of fluid flow properties, well geometry and flow rate on borehole pressures. For Bingham fluid flow one can observe that large pressures (compared with Newtonian fluid flow) are observed when constant flow rate are input as boundary condition. Pressure peaks caused by the acoustic wave propagation can be more intense in low compressible fluid flow, low viscosity
DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems
Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske
2008-12-01
We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly
DEFF Research Database (Denmark)
Guelbenzu, Gonzalo; Miao, Wang; Ben-Itzhak, Yaniv
2017-01-01
We present two hybrid fabrics integrating optical and electronic switches with SDN, and a novel approach improving the scaling of fast optical switches. C-Share reroute flows through optical switches increasing network performance. E-WDM exploits the optical switch transparency by emulating...
A Four-Step Block Hybrid Adams-Moulton Methods For The Solution ...
African Journals Online (AJOL)
This paper examines application of the Adam-Moulton's Method and proposes a modified self-starting continuous formula Called hybrid Adams-Moulton methods for the case k=4. It allows evaluation at both grid and off grid points to obtain the discrete schemes used in the block methods. The order, error constant and ...
Farinelli, R.; Ceccobello, C.; Romano, P.; Titarchuk, L.
2012-02-01
Context. Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. This requires developing numerical routines for the solution of the radiative equation according to the expected physical conditions of the systems under study. Aims: We have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. Methods: We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system τ using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. Results: We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth τ produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. Conclusions: The algorithm has been implemented in the xspec package for X-ray spectral fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (≳ 1012 G). This latter case is expected to be typical of accreting systems such as X
Zeebe, Richard E.
2017-11-01
I report results from accurate numerical integrations of solar system orbits over the past 100 Myr with the integrator package HNBody. The simulations used different integrator algorithms, step sizes, and initial conditions, and included effects from general relativity, different models of the Moon, the Sun’s quadrupole moment, and up to 16 asteroids. I also probed the potential effect of a hypothetical Planet 9, using one set of possible orbital elements. The most expensive integration (Bulirsch-Stoer) required 4 months of wall-clock time with a maximum relative energy error ≲ 3× {10}-13. The difference in Earth’s eccentricity ({{Δ }}{e}{ E }) was used to track the difference between two solutions, considered to diverge at time τ when max | {{Δ }}{e}{ E }| irreversibly crossed ˜10% of mean {e}{ E } ({{˜ }}0.028× 0.1). The results indicate that finding a unique orbital solution is limited by initial conditions from current ephemerides and asteroid perturbations to ˜54 Myr. Bizarrely, the 4-month Bulirsch-Stoer integration and a symplectic integration that required only 5 hr of wall-clock time (12-day time step, with the Moon as a simple quadrupole perturbation), agree to ˜63 Myr. Internally, such symplectic integrations are remarkably consistent even for large time steps, suggesting that the relationship between time step and τ is not a robust indicator of the absolute accuracy of symplectic integrations. The effect of a hypothetical Planet 9 on {{Δ }}{e}{ E } becomes discernible at ˜65 Myr. Using τ as a criterion, the current state-of-the-art solutions all differ from previously published results beyond ˜50 Myr. I also conducted an eigenmode analysis, which provides some insight into the chaotic nature of the inner solar system. The current study provides new orbital solutions for applications in geological studies. .
Fairnelli, R.; Ceccobello, C.; Romano, P.; Titarchuk, L.
2011-01-01
Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. This requires developing numerical routines for the solution of the radiative transfer equation according to the expected physical conditions of the systems under study. Aims. We have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. Methods. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system pi using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. Results. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth pi produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. Conclusions. The algorithm has been implemented in the XPEC package for X-ray fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (approx > 10(exp 12) G). This latter case is expected to be of typical accreting systems such as X
Energy Technology Data Exchange (ETDEWEB)
Murakami, Lelis Tetsuo
2008-07-01
Electrical power could be considered as one of the economy propulsion vector of a country, assuming extremely important and strategic role because it makes direct influence to the production capacity. The expansion of electrical energy production could not only be done in a short time because constructions in this area take many years and could require more then a decade depending on the magnitude of them. The national power generation group is constituted mainly by hydro power plants complemented by thermal power plants which use several kinds of fuel which generation cost is high, if compared to hydro power generation, and should be minimized. It is a complex planning issue to supply the future power demand which basically depends on the analysis of two compoundable scenarios: the first one refers to the forecast of future economy growing and in this case, unless un predicted issues occur such as the recent high economy growing experimented by China, the future demand does not show any surprise and is easy to predict; the second one, has inside the uncertainty because the hydro plants productions depends on the water quantity of rivers which depends on the past and current rainfall regimen. The quantity of rainfall is a stochastic data and follows the rules of probability and this drives to the study of cases and its deployments which are numerous causing difficulties to forecast the future. The planning of the electrical area has to examine the future demand and provide the necessary power generation equipment assuming a certain risk. To have it done, simulation models are used to predict the future, combining the two scenarios cited before, and viewing the results promoted by decision took in a step before. The difficult of this task is caused by the big amount of future alternatives provided by the combinatorial phenomena which require, to process the model, a computer with high processing capacity and specialized and specific methods that can resolve this
Directory of Open Access Journals (Sweden)
Wael M. Mohamed
2015-12-01
Full Text Available A numerical solution is presented for a one-dimensional, nonlinear boundary-value problem of thermoelasticity with variable volume force and heat supply in a slab. One surface of the body is subjected to a given periodic displacement and Robin thermal condition, while the other is kept fixed and at zero temperature. Other conditions may be equally treated as well. The volume force and bulk heating simulate the effect of a beam of hot particles infiltrating the medium. The present study is a continuation of previous work by the same authors for the half-space [1]. The presented Figures display the process of propagation and reflection of the coupled nonlinear thermoelastic waves in the slab. They also show the effects of volume force and heat supply on the distributions of the mechanical displacements and temperature inside the medium. The propagation of beats provides evidence for sufficiently large time values.
Sun, Shuyu
2012-06-02
A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.
Schlesinger, R. E.; Johnson, D. R.; Uccellini, L. W.
1983-01-01
In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.
Zhidkov, E P; Solovieva, T M
2001-01-01
The spectral problems with the eigenvalue-depending operator usually appear when the relative variants of the Schroedinger equation are considered in the impulse space. The eigenvalues and eigenfunctions calculation error caused by the numerical solving of such equations is the sum of the error entering the approximation of a continuous equation by the discrete equations systems with the help of the Bubnov-Galerkine method and the iterative method one. It is shown that the iterative method error is one-two order smaller than the problem of the discretisation one. Hence, the eigenvalues and eigenfunctions calculation accuracy of the spectral problem with the eigenvalue-depending operator is not worse than the linear spectral problem solution accuracy.
Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.
2018-01-01
The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.
Energy Technology Data Exchange (ETDEWEB)
Chang, Liang-Yi; Gershon, Talia S.; Haight, Richard A.; Lee, Yun Seog
2016-12-27
A hybrid vapor phase-solution phase CZT(S,Se) growth technique is provided. In one aspect, a method of forming a kesterite absorber material on a substrate includes the steps of: depositing a layer of a first kesterite material on the substrate using a vapor phase deposition process, wherein the first kesterite material includes Cu, Zn, Sn, and at least one of S and Se; annealing the first kesterite material to crystallize the first kesterite material; and depositing a layer of a second kesterite material on a side of the first kesterite material opposite the substrate using a solution phase deposition process, wherein the second kesterite material includes Cu, Zn, Sn, and at least one of S and Se, wherein the first kesterite material and the second kesterite material form a multi-layer stack of the absorber material on the substrate. A photovoltaic device and method of formation thereof are also provided.
Lipparini, Filippo; Scalmani, Giovanni; Lagardère, Louis; Stamm, Benjamin; Cancès, Eric; Maday, Yvon; Piquemal, Jean-Philip; Frisch, Michael J; Mennucci, Benedetta
2014-11-14
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.
Lipparini, Filippo; Scalmani, Giovanni; Lagardère, Louis; Stamm, Benjamin; Cancès, Eric; Maday, Yvon; Piquemal, Jean-Philip; Frisch, Michael J.; Mennucci, Benedetta
2014-11-01
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.
Energy Technology Data Exchange (ETDEWEB)
Lipparini, Filippo, E-mail: flippari@uni-mainz.de [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris (France); Sorbonne Universités, UPMC Univ. Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris (France); Sorbonne Universités, UPMC Univ. Paris 06, Institut du Calcul et de la Simulation, F-75005 Paris (France); Scalmani, Giovanni; Frisch, Michael J. [Gaussian, Inc., 340 Quinnipiac St. Bldg. 40, Wallingford, Connecticut 06492 (United States); Lagardère, Louis [Sorbonne Universités, UPMC Univ. Paris 06, Institut du Calcul et de la Simulation, F-75005 Paris (France); Stamm, Benjamin [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris (France); CNRS, UMR 7598 and 7616, F-75005 Paris (France); Cancès, Eric [Université Paris-Est, CERMICS, Ecole des Ponts and INRIA, 6 and 8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2 (France); Maday, Yvon [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris (France); Institut Universitaire de France, Paris, France and Division of Applied Maths, Brown University, Providence, Rhode Island 02912 (United States); Piquemal, Jean-Philip [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris (France); CNRS, UMR 7598 and 7616, F-75005 Paris (France); Mennucci, Benedetta [Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56126 Pisa (Italy)
2014-11-14
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.
Sun, Shuyu
2012-09-01
In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like MATLAB, Python, etc., which show to be more efficient for certain mathematical operations than for others. The proposed technique utilizes those operations in which these programming languages are efficient the most and keeps away as much as possible from those inefficient, time-consuming operations. In particular, this technique is based on the minimization of using multiple indices looping operations by reshaping the unknown variables into one-dimensional column vectors and performing the numerical operations using shifting matrices. The cell-centered information as well as the face-centered information are shifted to the adjacent face-center and cell-center, respectively. This enables the difference equations to be done for all the cells at once using matrix operations rather than within loops. Furthermore, for results post-processing, the face-center information can further be mapped to the physical grid nodes for contour plotting and stream lines constructions. In this work we apply this technique to flow and transport phenomena in porous media. © 2012 Elsevier Ltd.
Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.
2014-01-01
Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.
Hybrid method based on embedded coupled simulation of vortex particles in grid based solution
Kornev, Nikolai
2017-09-01
The paper presents a novel hybrid approach developed to improve the resolution of concentrated vortices in computational fluid mechanics. The method is based on combination of a grid based and the grid free computational vortex (CVM) methods. The large scale flow structures are simulated on the grid whereas the concentrated structures are modeled using CVM. Due to this combination the advantages of both methods are strengthened whereas the disadvantages are diminished. The procedure of the separation of small concentrated vortices from the large scale ones is based on LES filtering idea. The flow dynamics is governed by two coupled transport equations taking two-way interaction between large and fine structures into account. The fine structures are mapped back to the grid if their size grows due to diffusion. Algorithmic aspects of the hybrid method are discussed. Advantages of the new approach are illustrated on some simple two dimensional canonical flows containing concentrated vortices.
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Bassi, F. [Universita degli Studi di Ancona (Italy); Rebay, S. [Universita degli Studi di Brescia (Italy)
1997-03-01
This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. We extend a discontinuous finite element discretization originally considered for hyperbolic systems such as the Euler equations to the case of the Navier-Stokes equations by treating the viscous terms with a mixed formulation. The method combines two key ideas which are at the basis of the finite volume and of the finite element method, the physics of wave propagation being accounted for by means of Riemann problems and accuracy being obtained by means of high-order polynomial approximations within elements. As a consequence the method is ideally suited to compute high-order accurate solution of the Navier-Stokes equations on unstructured grids. The performance of the proposed method is illustrated by computing the compressible viscous flow on a flat plate and around a NACA0012 airfoil for several flow regimes using constant, linear, quadratic, and cubic elements. 23 refs., 24 figs., 3 tabs.
Ha, Sanghyun; Park, Junshin; You, Donghyun
2017-11-01
Utility of the computational power of modern Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. Due to its serial and bandwidth-bound nature, the present choice of numerical methods is considered to be a good candidate for evaluating the potential of GPUs for solving Navier-Stokes equations using non-explicit time integration. An efficient algorithm is presented for GPU acceleration of the Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution method used in the semi-implicit fractional-step method. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while Navier-Stokes equations are computed on a GPU. Extension to multiple NVIDIA GPUs is implemented using NVLink supported by the Pascal architecture. Performance of the present method is experimented on multiple Tesla P100 GPUs compared with a single-core Xeon E5-2650 v4 CPU in simulations of boundary-layer flow over a flat plate. Supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (Ministry of Science, ICT and Future Planning NRF-2016R1E1A2A01939553, NRF-2014R1A2A1A11049599, and Ministry of Trade, Industry and Energy 201611101000230).
Hajipour, Mojtaba; Jajarmi, Amin
2018-02-01
Using the Pontryagin's maximum principle for a time-delayed optimal control problem results in a system of coupled two-point boundary-value problems (BVPs) involving both time-advance and time-delay arguments. The analytical solution of this advance-delay two-point BVP is extremely difficult, if not impossible. This paper provides a discrete general form of the numerical solution for the derived advance-delay system by applying a finite difference θ-method. This method is also implemented for the infinite-time horizon time-delayed optimal control problems by using a piecewise version of the θ-method. A matrix formulation and the error analysis of the suggested technique are provided. The new scheme is accurate, fast and very effective for the optimal control of linear and nonlinear time-delay systems. Various types of finite- and infinite-time horizon problems are included to demonstrate the accuracy, validity and applicability of the new technique.
Kiah, M L Mat; Nabi, Mohamed S; Zaidan, B B; Zaidan, A A
2013-10-01
This study aims to provide security solutions for implementing electronic medical records (EMRs). E-Health organizations could utilize the proposed method and implement recommended solutions in medical/health systems. Majority of the required security features of EMRs were noted. The methods used were tested against each of these security features. In implementing the system, the combination that satisfied all of the security features of EMRs was selected. Secure implementation and management of EMRs facilitate the safeguarding of the confidentiality, integrity, and availability of e-health organization systems. Health practitioners, patients, and visitors can use the information system facilities safely and with confidence anytime and anywhere. After critically reviewing security and data transmission methods, a new hybrid method was proposed to be implemented on EMR systems. This method will enhance the robustness, security, and integration of EMR systems. The hybrid of simple object access protocol/extensible markup language (XML) with advanced encryption standard and secure hash algorithm version 1 has achieved the security requirements of an EMR system with the capability of integrating with other systems through the design of XML messages.
Wu, Jun-Yi; Chen, Show-An
2018-02-07
We use a mixed host, 2,6-bis[3-(carbazol-9-yl)phenyl]pyridine blended with 20 wt % tris(4-carbazoyl-9-ylphenyl)amine, to lower the hole-injection barrier, along with the bipolar and high-photoluminescence-quantum-yield (Φp= 84%), blue thermally activated delay fluorescence (TADF) material of 9,9-dimethyl-9,10-dihydroacridine-2,4,6-triphenyl-1,3,5-triazine (DMAC-TRZ) as a blue dopant to compose the emission layer for the fabrication of a TADF blue organic-light-emitting diode (BOLED). The device is highly efficient with the following performance parameters: maximum brightness (Bmax) = 57586 cd/m2, maximum current efficiency (CEmax) = 35.3 cd/A, maximum power efficiency (PEmax) = 21.4 lm/W, maximum external quantum efficiency (EQEmax) = 14.1%, and CIE coordinates (0.18, 0.42). This device has the best performance recorded among the reported solution-processed TADF BOLEDs and has a low efficiency roll-off: at brightness values of 1000 and 5000 cd/m2, its CEs are close, being 35.1 and 30.1 cd/A, respectively. Upon further doping of the red phosphor Ir(dpm)PQ2 (emission peak λmax = 595 nm) into the blue emission layer, we obtained a TADF-phosphor hybrid white organic-light-emitting diode (T-P hybrid WOLED) with high performance: Bmax = 43594 cd/m2, CEmax = 28.8 cd/A, PEmax = 18.1 lm/W, and CIE coordinates (0.38, 0.44). This Bmax = 43594 cd/m2 is better than that of the vacuum-deposited WOLED with a blue TADF emitter, 10000 cd/m2. This is also the first report on a T-P hybrid WOLED with a solution-processed emitting layer.
Kuba, N.; Murakami, M.
2010-01-01
The effect of hygroscopic seeding on warm rain clouds was examined using a hybrid cloud microphysical model combining a Lagrangian cloud condensation nuclei (CCN) activation model, a semi-Lagrangian droplet growth model, and an Eulerian spatial model for advection and sedimentation of droplets. This hybrid cloud microphysical model accurately estimated the effects of CCN on cloud microstructure and suggested the following conclusions for a moderate continental air mass (an air mass wit...
Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong
2017-10-01
In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.
Energy Technology Data Exchange (ETDEWEB)
Spoerl, Andreas
2008-06-05
Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)
Yang, Youlei; Xiang, Nong; Hu, Ye Min
2017-08-01
In recent experiments on the experimental advanced superconducting tokamak, the electron cyclotron wave and the two lower-hybrid waves at different frequencies, i.e., 4.6 GHz and 2.45 GHz, are applied simultaneously to sustain and control the plasma current. To investigate the synergy effects of the three waves, the Fokker-Planck equation with the quasi-linear diffusions induced by the three waves is solved numerically with the CQL3D code [R. W. Harvey and M. G. McCoy, in Proceedings of IAEA Technical Committee Meeting on Advances in Simulation and Modeling of Thermonuclear Plasmas, Montreal, Canada (1992)]. It is found that there might be strong synergy effects between the three waves. The electrons in the low velocity region in the velocity space can be accelerated perpendicularly by the electron cyclotron wave, and their parallel velocities can be increased due to scattering and fall into the resonance regions of the lower-hybrid waves. Therefore, such processes may bring more electrons to resonate with the lower-hybrid waves and enhance the current drive of the lower-hybrid waves. The synergy effects strongly depend on the distance between the resonance regions in the velocity space of the three waves.
Directory of Open Access Journals (Sweden)
Filip-Vacarescu Norin
2016-03-01
Full Text Available This paper discusses the concept of a hybrid damper made from a combination of two dissipative devices. A passive hysteretic device like steel Buckling Restrained Brace (BRB can be combined with a magneto-rheological (MR Fluid Damper in order to obtain a hybrid dissipative system. This system can work either as a semi-active system, if the control unit is available, or as a passive system, tuned for working according to performance based seismic engineering (PBSE scale of reference parameters (i.e. interstory drift.
Kida, Tetsuya; Matsufuji, Hiromasa; Yuasa, Masayoshi; Shimanoe, Kengo
2013-02-19
In recent years, the recovery of noble metals from waste has become very important because of their scarcity and increasing consumption. In this study, we attempt the photochemical recovery of noble metals from solutions using inorganic-organic hybrid photocatalysts. These catalysts are based on polyoxometalates such as PMo(12)O(40)(3-), SiW(12)O(40)(4-), and γ-SiW(10)O(36)(8-) coupled with a cationic surfactant, dimethyldioctadecylammonium (DODA). The three different photocatalysts dissolved in chloroform were successful in photoreducing gold ions dissolved in water in a two-phase (chloroform/water) system under UV irradiation (λ SiW(10)O(36)/DODA photocatalyst exhibited the best activity and recovered gold from solution efficiently. It was suggested that one-electron reduced γ-SiW(10)O(36)(9-) formed by the UV irradiation reduced gold ions. As a result, large two-dimensional particles (gold nanosheets) were produced using the γ-SiW(10)O(36)/DODA photocatalyst, indicating that the reduction of gold ions occurred at the interface between chloroform and water. The γ-SiW(10)O(36)/DODA photocatalyst was able to recover metals such as platinum, silver, palladium, and copper from deaerated solutions. The selective recovery of gold is possible by controlling pH and oxygen concentration in the reaction system.
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Yuli Chen
2014-01-01
Full Text Available The electrical percolation of polymer-matrix composites (PMCs containing hybrid fillers of carbon nanotubes (CNTs and carbon black (CB is estimated by studying the connection possibility of the fillers using Monte Carlo simulation. The 3D simulation model of CB-CNT hybrid filler is established, in which CNTs are modeled by slender capped cylinders and CB groups are modeled by hypothetical spheres with interspaces because CB particles are always agglomerated. The observation on the effects of CB and CNT volume fractions and dimensions on the electrical percolation threshold of hybrid filled composites is then carried out. It is found that the composite electrical percolation threshold can be reduced by increasing CNT aspect ratio, as well as increasing the diameter ratio of CB groups to CNTs. And adding CB into CNT composites can decrease the CNT volume needed to convert the composite conductivity, especially when the CNT volume fraction is close to the threshold of PMCs with only CNT filler. Different from previous linear assumption, the nonlinear relation between CB and CNT volume fractions at composite percolation threshold is revealed, which is consistent with the synergistic effect observed in experiments. Based on the nonlinear relation, the estimating equation for the electrical percolation threshold of the PMCs containing CB-CNT hybrid fillers is established.
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Kevin G McCracken
Full Text Available Hybridization is common between species of animals, particularly in waterfowl (Anatidae. One factor shown to promote hybridization is restricted mate choice, which can occur when 2 species occur in sympatry but one is rare. According to the Hubbs principle, or "desperation hypothesis," the rarer species is more likely to mate with heterospecifics. We report the second of 2 independent examples of hybridization between 2 species of ducks inhabiting island ecosystems in the Subantarctic and South Atlantic Ocean. Yellow-billed pintails (Anas georgica and speckled teal (Anas flavirostris are abundant in continental South America, where they are sympatric and coexist in mixed flocks. But on South Georgia, an isolated island in the Subantarctic, the pintail population of approximately 6000 pairs outnumbers a small breeding population of speckled teal 300∶1. Using 6 genetic loci (mtDNA and 5 nuclear introns and Bayesian assignment tests coupled with coalescent analyses, we identified hybrid-origin speckled teal alleles in 2 pintails on South Georgia. While it is unclear whether introgression has also occurred into the speckled teal population, our data suggest that this hybridization was not a recent event, but occurred some time ago. We also failed to identify unequivocal evidence of introgression in a much larger sample of pintails and speckled teal from Argentina using a 3-population "Isolation-with-Migration" coalescent analysis. Combined with parallel findings of hybridization between these same 2 duck species in the Falkland Islands, where population ratios are reversed and pintails are outnumbered by speckled teal 1:10, our results provide further support for the desperation hypothesis, which predicts that scarcity in one population and abundance of another will often lead to hybridization. While the South Georgia pintail population appears to be thriving, it's possible that low density of conspecific mates and inverse density dependence
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L. Malgaca
2009-01-01
Full Text Available Piezoelectric smart structures can be modeled using commercial finite element packages. Integration of control actions into the finite element model solutions (ICFES can be done in ANSYS by using parametric design language. Simulation results can be obtained easily in smart structures by this method. In this work, cantilever smart structures consisting of aluminum beams and lead-zirconate-titanate (PZT patches are considered. Two cases are studied numerically and experimentally in parallel. In the first case, a smart structure with a single PZT patch is used for the free vibration control under an initial tip displacement. In the second case, a smart structure with two PZT patches is used for the forced vibration control under harmonic excitation, where one of the PZT patches is used as vibration generating shaker while the other is used as vibration controlling actuator. For the two cases, modal analyses are done using chirp signals; Control OFF and Control ON responses in the time domain are obtained for various controller gains. A non-contact laser displacement sensor and strain gauges are utilized for the feedback signals. It is observed that all the simulation results agree with the experimental results.
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Muhammad Awais
Full Text Available Analysis has been done to investigate the heat generation/absorption effects in a steady flow of non-Newtonian nanofluid over a surface which is stretching linearly in its own plane. An upper convected Maxwell model (UCM has been utilized as the non-Newtonian fluid model in view of the fact that it can predict relaxation time phenomenon which the Newtonian model cannot. Behavior of the relaxations phenomenon has been presented in terms of Deborah number. Transport phenomenon with convective cooling process has been analyzed. Brownian motion "Db" and thermophoresis effects "Dt" occur in the transport equations. The momentum, energy and nanoparticle concentration profiles are examined with respect to the involved rheological parameters namely the Deborah number, source/sink parameter, the Brownian motion parameters, thermophoresis parameter and Biot number. Both numerical and analytic solutions are presented and found in nice agreement. Comparison with the published data is also made to ensure the validity. Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.
Energy Technology Data Exchange (ETDEWEB)
Cheng, C.Z.
1988-12-01
A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, theta, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle theta and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ideal MHD codes show that the NOVA code converges faster and gives more accurate results. An extended version of NOVA is developed to integrate non-Hermitian eigenmode equations due to energetic particles. The set of non-Hermitian integro-differential eigenmode equations is numerically solved by the NOVA-K code. We have studied the problems of the stabilization of ideal MHD internal kink modes by hot particle pressure and the excitation of ''fishbone'' internal kink modes by resonating with the energetic particle magnetic drift frequency. Comparisons with analytical solutions show that the values of the critical ..beta../sub h/ from the analytical theory can be an order of magnitude different from those computed by the NOVA-K code. 24 refs., 11 figs., 1 tab.
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M. Golzar
2014-01-01
Full Text Available Recently, iron nanoparticles have attracted more attention for groundwater remediation due to its potential to reduce subsurface contaminants such as PCBs, chlorinated solvents, and heavy metals. The magnetic properties of iron nanoparticles cause to attach to each other and form bigger colloid particles of iron nanoparticles with more rapid sedimentation rate in aqueous environment. Using the surfactants such as poly acrylic acid (PAA prevents iron nanoparticles from forming large flocs that may cause sedimentation and so increases transport distance of the nanoparticles. In this study, the transport of iron oxide nanoparticles (Fe3O4 stabilized with PAA in a one-dimensional porous media (column was investigated. The slurries with concentrations of 20,100 and 500 (mg/L were injected into the bottom of the column under hydraulic gradients of 0.125, 0.375, and 0.625. The results obtained from experiments were compared with the results obtained from numerical solution of advection-dispersion equation based on the classical colloid filtration theory (CFT. The experimental and simulated breakthrough curves showed that CFT is able to predict the transport and fate of iron oxide nanoparticles stabilized with PAA (up to concentration 500 ppm in a porous media.
Ke, Qiutan; Wu, Qian; Liang, Lijuan; Pei, Yanli; Lu, Xubing; Li, Minmin; Huang, Kairong; Liu, Xuying; Liu, Chuan
2017-10-01
In organic thin-film transistors (OTFTs), using high-k dielectrics could increase the accumulated carrier numbers at low operation voltage (i.e. the bulk effect), but may induce extra dipolar disorders to affect the electronic states in organic semiconductors (i.e. the interfacial effect). The two effects are considered together to model charge transport in OTFTs and to give quantitative calculations of the impacts from using high-k dielectrics or hybrid dielectrics, especially the relations between mobility and Fermi-energy, carrier concentrations, or gate-voltage. In experimental studies, zirconium oxide (ZrO2) and yttrium oxide (Y2O3) are fabricated by solution process for high-k dielectrics. The oxide insulating films are modified by low-k polymer layers and the resulting OTFTs show low operation voltage and high performance in ambient test. The highest mobility reaches 2.38 cm2 V-1 s-1 for ZrO2 based OTFT and 3.56 cm2 V-1 s-1 for Y2O3 based OTFT, and the on/off ratio is 1.4 × 104 for ZrO2 devices and 5.4 × 104 for Y2O3 devices. In general, the trends of experimentally measured mobility are consistent with the theoretical calculations, showing the high-k/low-k hybrid dielectrics mainly improve the carrier mobility in the regime of low carrier density.
The Solution of Two-Phase Inverse Stefan Problem Based on a Hybrid Method with Optimization
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Yang Yu
2015-01-01
Full Text Available The two-phase Stefan problem is widely used in industrial field. This paper focuses on solving the two-phase inverse Stefan problem when the interface moving is unknown, which is more realistic from the practical point of view. With the help of optimization method, the paper presents a hybrid method which combines the homotopy perturbation method with the improved Adomian decomposition method to solve this problem. Simulation experiment demonstrates the validity of this method. Optimization method plays a very important role in this paper, so we propose a modified spectral DY conjugate gradient method. And the convergence of this method is given. Simulation experiment illustrates the effectiveness of this modified spectral DY conjugate gradient method.
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Ambarish Panda
2016-09-01
Full Text Available A new evolutionary hybrid algorithm (HA has been proposed in this work for environmental optimal power flow (EOPF problem. The EOPF problem has been formulated in a nonlinear constrained multi objective optimization framework. Considering the intermittency of available wind power a cost model of the wind and thermal generation system is developed. Suitably formed objective function considering the operational cost, cost of emission, real power loss and cost of installation of FACTS devices for maintaining a stable voltage in the system has been optimized with HA and compared with particle swarm optimization algorithm (PSOA to prove its effectiveness. All the simulations are carried out in MATLAB/SIMULINK environment taking IEEE30 bus as the test system.
Problems and solutions in high-rate multichannel hybrid photodiode design The CMS experience
Cushman, P B
2002-01-01
The unique conditions of the CMS experiment (4 T magnetic field, restricted access, high neutron radiation, and 25-ns bunch-crossings) necessitated the development of a new type of high-rate multichannel hybrid photodiode for the tile/fiber hadronic calorimeter. New complexities arose in the push toward high-rate operation, necessitating design changes in the diode structure and surface treatment. The product is now capable of high-rate operation with low crosstalk and leakage current. Lifetime studies of high-voltage behavior, total charge, and irradiation have shown that the tubes will survive the ten years of CMS running with only a few percent change in gain and manageable leakage current rise. (13 refs).
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Parovik Roman I.
2016-09-01
Full Text Available The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.
Tapsanit, Piyawath; Ishihara, Teruya; Otani, Chiko
2016-01-01
We present quasi-analytical solutions (QANS) of hybrid platform (HP) comprising metallic grating (MG) and stacked-dielectric layers for terahertz (THz) radiation. The QANS are validated by finite difference time domain simulation. It is found that the Wood anomalies induce the high-order spoof surface plasmon resonances in the HP. The QANS are applied to optimize new perfect absorber for THz sensing of large-area thin film with ultrahigh figure of merit reaching fifth order of magnitude for the film thickness 0.0001p (p: MG period). The first-order Wood's anomaly of the insulator layer and the Fabry-Perot in the slit's cavity account for the resonance of the perfect absorber. The QANS and the new perfect absorber may lead to highly sensitive and practical nano-film refractive index sensor for THz radiation.
An All-Solution-Based Hybrid CMOS-Like Quantum Dot/Carbon Nanotube Inverter
Shulga, Artem G.; Derenskyi, Vladimir; Salazar-Rios, Jorge Mario; Dirin, Dmitry N.; Fritsch, Martin; Kovalenko, Maksym V.; Scherf, Ullrich; Loi, Maria A.
2017-01-01
The development of low-cost, flexible electronic devices is subordinated to the advancement in solution-based and low-temperature-processable semiconducting materials, such as colloidal quantum dots (QDs) and single-walled carbon nanotubes (SWCNTs). Here, excellent compatibility of QDs and SWCNTs as
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N. A. Ahmad
2017-01-01
Full Text Available A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived methods in comparison with other existing Runge-Kutta (RK methods.
Gaudillat, Pierre; Jurin, Florian; Lakard, Boris; Buron, Cédric; Suisse, Jean-Moïse; Bouvet, Marcel
2014-01-01
We have prepared different hybrid polymer-phthalocyanine materials by solution processing, starting from two sulfonated phthalocyanines, s-CoPc and CuTsPc, and polyvinylpyrrolidone (PVP), polyethylene glycol (PEG), poly(acrylic acid-co-acrylamide) (PAA-AM), poly(diallyldimethylammonium chloride) (PDDA) and polyaniline (PANI) as polymers. We also studied the response to ammonia (NH3) of resistors prepared from these sensing materials. The solvent casted films, prepared from s-CoPc and PVP, PEG and PAA-AM, were highly insulating and very sensitive to the relative humidity (RH) variation. The incorporation of s-CoPc in PDDA by means of layer-by-layer (LBL) technique allowed to stabilize the film, but was too insulating to be interesting. We also prepared PANI-CuTsPc hybrid films by LBL technique. It allowed a regular deposition as evidenced by the linear increase of the absorbance at 688 nm as a function of the number of bilayers. The sensitivity to ammonia (NH3) of PANi-CuTsPc resistors was very high compared to that of individual materials, giving up to 80% of current decrease when exposed to 30 ppm NH3. Contrarily to what happens with neutral polymers, in PANI, CuTsPc was stabilized by strong electrostatic interactions, leading to a stable response to NH3, whatever the relative humidity in the range 10%–70%. Thus, the synergy of PANI with ionic macrocycles used as counteranions combined with their simple aqueous solution processing opens the way to the development of new gas sensors capable of operating in real world conditions. PMID:25061841
Kim, Donghyeon; Jeon, Joonhyeon
2015-01-01
Zinc-bromine flow battery using aqueous electrolyte has advantages of cost effective and high energy density, but there still remains a problem improving stability and durability of electrolyte materials during long-time cell operation. This paper focuses on providing a homogeneous aqueous solution for durability and stability of zinc bromide electrolyte. For performance experiments of conventional and proposed electrolyte solutions, detailed cyclic voltammetry (CV) measurements (at a scan rate of 20 mV s-1 in the range of -1.5 V~1.5 V) are carried out for 40 cycles and five kinds of electrolytes containing which has one of additives, such as (conventionally) zinc chloride, potassium chloride, (newly) lithium perchlorate, sodium perchlorate and zeolite-Y are compared with the 2.0 M ZnBr2 electrolyte, respectively. Experimental results show that using the proposed three additives provides higher anodic and cathodic peak current density of electrolytes than using other two conventional additives, and can lead to improved chemical reversibility of zinc bromide electrolyte. Especially, the solution of which the zeolite-Y added, shows enhanced electrochemical stability of zinc bromide electrolyte. Consequently, proposed electrolytes have a significant advantage in comparison with conventional electrolytes on higher stability and durability.